{"title":"Functional Analysis","description":"\u003cp\u003eFunctional analysis is a branch of mathematics focused on the study of vector spaces, operators, and functions with infinite dimensions or complex structures. It provides rigorous frameworks for analyzing linear transformations, convergence, and continuity—making it central to modern mathematical research, physics, engineering, and applied sciences. Distinct from general mathematics, functional analysis specializes in abstract spaces such as Hilbert and Banach spaces, exploring deep relationships between algebraic and topological concepts.\u003c\/p\u003e\u003cp\u003eUse this subject to concentrate on resources that specifically address the principles and applications unique to functional analysis. If you’re seeking foundational texts, advanced theoretical works, or connections to applied mathematics, narrowing your exploration here—rather than in the broader mathematics category—will help you focus on concepts relevant to infinite-dimensional analysis and their diverse mathematical implications.\u003c\/p\u003e","products":[{"product_id":"selected-topics-generalized-integration-9789819812196-new","title":"Selected Topics on Generalized Integration","description":"\u003cp\u003eThis comprehensive volume offers an in-depth exploration of advanced integration theories, extending beyond classical methods to unify and expand the field. Building on the foundational work of Jaroslav Kurzweil and Ralph Henstock, the book delves into the Henstock-Kurzweil and McShane gauge integrals, presenting a more intuitive and versatile alternative to the traditional Lebesgue integral. By bridging gaps in existing literature, the authors provide a rigorous treatment of integration on metric measure spaces, exploring critical concepts such as completeness, compactness, and Cousin's lemma.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe book systematically introduces advanced topics, including the variational Henstock integral in locally convex spaces, the Riemann-Lebesgue integral for vector-valued functions, and generalizations of the Sugeno integral. Further chapters explore convergence in Banach spaces on time scales, set-valued integrals, and applications to harmonic analysis and partial differential equations, including solutions to the heat equation in distribution spaces.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eNotably, the text presents innovative approaches like the symmetric Laplace integral and the q-Homotopy Analysis Method for solving nonlinear integral equations, offering practical tools for modern analysis. Unified integral representations for generalized Mittag-Leffler functions further highlight the book's engagement with special functions.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eIdeal for researchers and advanced students in mathematical analysis, this book seamlessly integrates classical theories with modern advancements, offering both theoretical insights and practical applications across mathematics, physics, and engineering.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543605641506,"sku":"9789819812196-new","price":113.45,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789819812196.jpg?v=1776386170"},{"product_id":"selected-lectures-functional-analysis-9789819803514-new","title":"Selected Lectures on Functional Analysis","description":"\u003cp\u003eThe main aim of this book is to provide an advanced textbook on functional analysis, focusing on the functional calculus of operators. Based on basic knowledge of functional analysis on metric spaces and linear bounded operators, this book systematically introduces the spectral theory of operators and the theory of operator semigroups, including Banach algebras, spectral theories of both bounded and unbounded linear operators, as well as semigroups of operators. They play important roles in various areas of modern mathematics such as harmonic analysis, partial differential equations, probability and statistics, engineering science, quantum physics, and statistical mechanics.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis book provides rich examples and exercises, emphasizing the combination of the theory and examples to enhance readers' ability to apply functional analysis theory to solve related problems. Compared with many other functional analysis textbooks, this book focuses on the spectral theory and the operator semigroup theory, serving as an appropriate connection for functional analysis between undergraduate and graduate levels, making it an ideal textbook for both. It will also be a good reference book for researchers who are interested in modern analysis, such as functional analysis, harmonic analysis, and partial differential equations.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543609540898,"sku":"9789819803514-new","price":206.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789819803514.jpg?v=1776386307"},{"product_id":"lipschitz-algebras-2nd-ed-9789814740630-new","title":"Lipschitz Algebras (Second Edition)","description":"\u003cp\u003eThis is the standard reference on algebras of Lipschitz functions, written by the leading figure in the field. The second edition includes new chapters on nonlinear Banach space geometry, differentiability in metric measure spaces, and quantum metrics. This latest material reflects the importance of spaces of Lipschitz functions in a diverse range of current research directions. Every functional analyst should have some knowledge of this subject.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543614587170,"sku":"9789814740630-new","price":178.92,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814740630.jpg?v=1776386584"},{"product_id":"functional-analysis-2nd-ed-9789814733922-new","title":"Functional Analysis (2nd Ed)","description":"\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cstrong\u003e\u003cem\u003eReviews of the First Edition: \u003c\/em\u003e\u003c\/strong\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003e\"This is a well-written student-friendly basic introduction to functional analysis and Hilbert space ...\"\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003eMAA Online Book Review\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003e\u003cem\u003e\"The highlight of the book is the spectral theorem for selfadjoint linear compact operators, presented with full proof. The book ends with a set of well chosen exercises completing the main text.\"\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003eZentralblatt MATH\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis book presents basic elements of the theory of Hilbert spaces and operators on Hilbert spaces, culminating in a proof of the spectral theorem for compact, self-adjoint operators on separable Hilbert spaces. It exhibits a construction of the space of \u003cem\u003epth\u003c\/em\u003e power Lebesgue integrable functions by a completion procedure with respect to a suitable norm in a space of continuous functions, including proofs of the basic inequalities of H\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543615439138,"sku":"9789814733922-new","price":61.48,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814733922.jpg?v=1776386647"},{"product_id":"kurzweil-stieltjes-integral-theory-applications-9789814641777-new","title":"Kurzweil-Stieltjes Integral: Theory and Applications","description":"\u003cp\u003eThe book is primarily devoted to the Kurzweil-Stieltjes integral and its applications in functional analysis, theory of distributions, generalized elementary functions, as well as various kinds of generalized differential equations, including dynamic equations on time scales. It continues the research that was paved out by some of the previous volumes in the \u003cem\u003eSeries in Real Analysis\u003c\/em\u003e. Moreover, it presents results in a thoroughly updated form and, simultaneously, it is written in a widely understandable way, so that it can be used as a textbook for advanced university or PhD courses covering the theory of integration or differential equations.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543644242210,"sku":"9789814641777-new","price":155.02,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814641777.jpg?v=1776387750"},{"product_id":"tropical-value-distribution-theory-ultra-discrete-equation-9789814632799-new","title":"Tropical Value Distribution Theory \u0026 Ultra-Discrete Equation","description":"\u003cp\u003eThis is the first textbook-type presentation of tropical value distribution theory. It provides a detailed introduction of the tropical version of the Nevanlinna theory, describing growth and value distribution analysis of continuous, piecewise linear functions on the real axis. The book also includes applications of this theory to ultra-discrete equations. Three appendices are given to compare the contents of the theory with the classical counterparts in complex analysis.\u003c\/p\u003e\u003cp\u003eDetailed presentation of the proofs makes the book accessible for lecture courses and independent studies at the graduate and post-doctoral level.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543646208290,"sku":"9789814632799-new","price":119.68,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814632799.jpg?v=1776387871"},{"product_id":"real-analysis-3rd-ed-9789814578547-new","title":"Real Analysis (3rd Ed)","description":"\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped. The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians.\u003c\/p\u003e\u003cp\u003eThe book is also very helpful to graduate students in statistics and electrical engineering, two disciplines that apply measure theory.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543664918818,"sku":"9789814578547-new","price":90.61,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814578547.jpg?v=1776388593"},{"product_id":"problems-proofs-real-analysis-9789814578509-new","title":"Problems and Proofs in Real Analysis","description":"This volume consists of the proofs of 391 problems in Real Analysis: Theory of Measure and Integration (3rd Edition).Most of the problems in Real Analysis are not mere applications of theorems proved in the book but rather extensions of the proven theorems or related theorems. Proving these problems tests the depth of understanding of the theorems in the main text.This volume will be especially helpful to those who read Real Analysis in self-study and have no easy access to an instructor or an advisor.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543664984354,"sku":"9789814578509-new","price":71.89,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814578509.jpg?v=1776388595"},{"product_id":"measure-theory-functional-analysis-9789814508568-new","title":"Measure Theory and Functional Analysis","description":"This book provides an introduction to measure theory and functional analysis suitable for a beginning graduate course, and is based on notes the author had developed over several years of teaching such a course. It is unique in placing special emphasis on the separable setting, which allows for a simultaneously more detailed and more elementary exposition, and for its rapid progression into advanced topics in the spectral theory of families of self-adjoint operators. The author's notion of measurable Hilbert bundles is used to give the spectral theorem a particularly elegant formulation not to be found in other textbooks on the subject.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543673536802,"sku":"9789814508568-new","price":92.66,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814508568.jpg?v=1776389050"},{"product_id":"fixed-point-theorems-their-applications-9789814458917-new","title":"Fixed Point Theorems and Their Applications","description":"Introduction -- 1. Early fixed point theorems. 1.1. The Picard-Banach theorem. 1.2. Vector fields on spheres. 1.3. Proof of the Brouwer theorem and corollaries. 1.4. Fixed point theorems for groups of affine maps of [symbol] -- 2. Fixed point theorems in analysis. 2.1. The Schaüder-Tychonoff theorem. 2.2. Applications of the Schaüder-Tychonoff theorem. 2.3. The theorems of Hahn, Kakutani and Markov-Kakutani. 2.4. Amenable groups -- 3. The Lefschetz fixed point theorem. 3.1. The Lefschetz theorem for compact polyhedra. 3.2. The Lefschetz theorem for a compact manifold. 3.3. Proof of the Lefschetz theorem. 3.4. Some applications. 3.5. The Atiyah-Bott fixed point theorem -- 4. Fixed point theorems in geometry. 4.1. Some generalities on Riemannian manifolds. 4.2. Hadamard manifolds and Cartan's theorem. 4.3. Fixed point theorems for compact manifolds -- 5. Fixed points of volume preserving maps. 5.1. The Poincaré recurrence theorem. 5.2. Symplectic geometry and its fixed point theorems. 5.3. Poincaré's last geometric theorem. 5.4. Automorphisms of Lie algebras. 5.5. Hyperbolic automorphisms of a manifold. 5.6. The Lefschetz zeta function -- 6. Borel's fixed point theorem in algebraic groups. 6.1. Complete varieties and Borel's theorem. 6.2. The projective and Grassmann spaces. 6.3. Projective varieties. 6.4. Consequences of Borel's fixed point. 6.5. Two conjugacy theorems for real linear Lie groups -- 7. Miscellaneous fixed point theorems. 7.1. Applications to number theory. 7.2. Fixed points in group theory. 7.3. A fixed point theorem in complex analysis -- 8. A fixed point theorem in set theory -- Afterword","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543675502882,"sku":"9789814458917-new","price":93.7,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814458917.jpg?v=1776389165"},{"product_id":"nonstandard-methods-functional-anal-9789814287548-new","title":"Nonstandard Methods in Functional Anal..","description":"In the early 1960s, by using techniques from the model theory of first-order logic, Robinson gave a rigorous formulation and extension of Leibniz' infinitesimal calculus. Since then, the methodology has found applications in a wide spectrum of areas in mathematics, with particular success in the probability theory and functional analysis. In the latter, fruitful results were produced with Luxemburg's invention of the nonstandard hull construction. However, there is still no publication of a coherent and self-contained treatment of functional analysis using methods from nonstandard analysis. This publication aims to fill this gap.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543766073634,"sku":"9789814287548-new","price":107.22,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789814287548.jpg?v=1776391737"},{"product_id":"weighted-inequalities-involving-quasiconcave-operators-9789813239623-new","title":"Weighted Inequalities Involving ?-Quasiconcave Operators","description":"\u003cp\u003eSome problems in mathematical analysis (e.g., in theory of function spaces, in approximation theory or in interpolation theory) lead to the investigation of weighted inequalities on certain classes of quasiconcave functions on the interval \u003cem\u003eI=(a, b)\u003c\/em\u003e ∊ \u003cem\u003e\u003cstrong\u003eR\u003c\/strong\u003e\u003c\/em\u003e. In this book we analyse the class \u003cem\u003eQρ(I)\u003c\/em\u003e of \u003cem\u003eρ\u003c\/em\u003e-quasiconcave functions in a complete generality in order to establish results needed for a comprehensive study of weighted inequalities on the class \u003cem\u003eQρ(I)\u003c\/em\u003e. We illustrate our results on weighted inequalities of Hardy type, on weighted inequalities of Hardy type involving supremum, and on reverse forms of these inequalities.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543885775138,"sku":"9789813239623-new","price":103.05,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813239623.jpg?v=1776393487"},{"product_id":"operator-theory-problem-book-9789813236257-new","title":"An Operator Theory Problem Book","description":"\u003cp\u003eThis book is for third and fourth year university mathematics students (and Master students) as well as lecturers and tutors in mathematics and anyone who needs the basic facts on Operator Theory (e.g. Quantum Mechanists). The main setting for bounded linear operators here is a Hilbert space. There is, however, a generous part on General Functional Analysis (not too advanced though). There is also a chapter on Unbounded Closed Operators.\u003c\/p\u003e\u003cp\u003eThe book is divided into two parts. The first part contains essential background on all of the covered topics with the sections: True or False Questions, Exercises, Tests and More Exercises. In the second part, readers may find answers and detailed solutions to the True or False Questions, Exercises and Tests.\u003c\/p\u003e\u003cp\u003eAnother virtue of the book is the variety of the topics and the exercises and the way they are tackled. In many cases, the approaches are different from what is known in the literature. Also, some very recent results from research papers are included.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543894262050,"sku":"9789813236257-new","price":134.25,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813236257.jpg?v=1776393693"},{"product_id":"abstract-duality-pairs-analysis-9789813232761-new","title":"Abstract Duality Pairs in Analysis","description":"\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe book presents a theory of abstract duality pairs which arises by replacing the scalar field by an Abelian topological group in the theory of dual pair of vector spaces. Examples of abstract duality pairs are vector valued series, spaces of vector valued measures, spaces of vector valued integrable functions, spaces of linear operators and vector valued sequence spaces. These examples give rise to numerous applications such as abstract versions of the Orlicz-Pettis Theorem on subseries convergent series, the Uniform Boundedness Principle, the Banach-Steinhaus Theorem, the Nikodym Convergence theorems and the Vitali-Hahn-Saks Theorem from measure theory and the Hahn-Schur Theorem from summability. There are no books on the current market which cover the material in this book. Readers will find interesting functional analysis and the many applications to various topics in real analysis.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543905698082,"sku":"9789813232761-new","price":123.83,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813232761.jpg?v=1776394083"},{"product_id":"operator-functions-operator-equations-9789813221260-new","title":"Operator Functions and Operator Equations","description":"\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis book is devoted to norm estimates for operator-valued functions of one and two operator arguments, as well as to their applications to spectrum perturbations of operators and to linear operator equations, i.e. to equations whose solutions are linear operators. Linear operator equations arise in both mathematical theory and engineering practice. The norm estimates suggested in the book have applications to the theories of ordinary differential, difference, functional-differential and integro-differential equations, as well as to the theories of integral operators and analytic functions. This book provides new tools for specialists in matrix theory and functional analysis. A significant part of the book covers the theory of triangular representations of operators that was developed by L de Branges, M S Brodskii, I C Gohberg, M G Krein, M S Livsic and other mathematicians.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543933747490,"sku":"9789813221260-new","price":103.05,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813221260.jpg?v=1776395001"},{"product_id":"functional-equations-inequalities-9789813149977-new","title":"Functional Equations and Inequalities","description":"\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThis volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51543998169378,"sku":"9789813149977-new","price":61.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813149977.jpg?v=1776395730"},{"product_id":"inequa-anal-probab-2nd-ed-9789813143982-new","title":"Inequalities in Analysis and Probability (Second Edition)","description":"\u003cp\u003e\u003cem\u003e\"The strongest part of the book is the discussion in Chapter 4 of martingale inequalities, mainly various versions of the Burkholder-Davis-Gundy inequality.\"\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e\u003cem\u003eMathematical Reviews\u003c\/em\u003e\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe book is aimed at graduate students and researchers with basic knowledge of Probability and Integration Theory. It introduces classical inequalities in vector and functional spaces with applications to probability. It also develops new extensions of the analytical inequalities, with sharper bounds and generalizations to the sum or the supremum of random variables, to martingales and to transformed Brownian motions. The proofs of many new results are presented in great detail. Original tools are developed for spatial point processes and stochastic integration with respect to local martingales in the plane.\u003c\/p\u003e\u003cp\u003eThis second edition covers properties of random variables and time continuous local martingales with a discontinuous predictable compensator, with exponential inequalities and new inequalities for their maximum variable and their \u003cem\u003ep\u003c\/em\u003e-variations. A chapter on stochastic calculus presents the exponential sub-martingales developed for stationary processes and their properties. Another chapter devoted itself to the renewal theory of processes and to semi-Markovian processes, branching processes and shock processes. The Chapman-Kolmogorov equations for strong semi-Markovian processes provide equations for their hitting times in a functional setting which extends the exponential properties of the Markovian processes.\u003c\/p\u003e","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544014094626,"sku":"9789813143982-new","price":115.53,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789813143982.jpg?v=1776396097"},{"product_id":"nonnegative-matrice-positive-operators-9789812839176-new","title":"Nonnegative Matrice, Positive Operators..","description":"Nonnegative matrices and positive operators are widely applied in science, engineering, and technology. 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In addition, it serves as a good reference for researchers in mathematical sciences, physical sciences, and engineering.","brand":"WORLD SCIENTIFIC PUB CO INC","offers":[{"title":"New","offer_id":51544060756258,"sku":"9789812839176-new","price":98.91,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0893\/4755\/5618\/files\/9789812839176.jpg?v=1776396909"},{"product_id":"value-distribution-ultrametric-analysis-applications-9789811298325-new","title":"Value Distribution in Ultrametric Analysis and Applications","description":"\u003cp\u003eAfter a construction of the complete ultrametric fields K, the book presents most of properties of analytic and meromorphic functions in K: algebras of analytic elements, power series in a disk, order, type and cotype of growth of entire functions, clean functions, question on a relation true for clean functions, and a counter-example on a non-clean function. Transcendence order and transcendence type are examined with specific properties of certain p-adic numbers.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe Kakutani problem for the \"corona problem\" is recalled and multiplicative semi-norms are described. Problems on exponential polynomials, meromorphic functions are introduced and the Nevanlinna Theory is explained with its applications, particularly to problems of uniqueness. Injective analytic elements and meromorphic functions are examined and characterized through a relation.\u003c\/p\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eThe Nevanlinna Theory out of a hole is described. Many results on zeros of a meromorphic function and its derivative are examined, particularly the solution of the Hayman conjecture in a P-adic field is given. Moreover, if a meromorphic functions in all the field, admitting primitives, admit a Picard value, then it must have enormously many poles. 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