Convolution Type Functional Equations On Topological Abelian Groups
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Convolution Type Functional Equations On Topological Abelian Groups
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Author : L szl¢ Szkelyhidi
language : en
Publisher: World Scientific
Release Date : 1991
Convolution Type Functional Equations On Topological Abelian Groups written by L szl¢ Szkelyhidi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
This book is devoted to the possible applications of spectral analysis and spectral synthesis for convolution type functional equations on topological abelian groups. The solution space of convolution type equations has been synthesized in the sense that the general solutions are built up from exponential monomial solutions. In particular, equivalence of systems of functional equations can be tested. This leads to a unified treatment of classical equations and to interesting new results.
Convolution Type Functional Equations On Topological Abelian Groups
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Author : László Székelyhidi
language : en
Publisher: World Scientific
Release Date : 1991-04-22
Convolution Type Functional Equations On Topological Abelian Groups written by László Székelyhidi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-04-22 with Mathematics categories.
This book is devoted to the possible applications of spectral analysis and spectral synthesis for convolution type functional equations on topological abelian groups. The solution space of convolution type equations has been synthesized in the sense that the general solutions are built up from exponential monomial solutions. In particular, equivalence of systems of functional equations can be tested. This leads to a unified treatment of classical equations and to interesting new results. Contents:The Basic Problems of Spectral Analysis and Spectral SynthesisPolynomials and Exponential PolynomialsFourier-Transformation and Mean Periodic FunctionsApplications for Functional Equations:Functional Equations for PolynomialsThe Levi-Civitá Functional EquationD'Alembert-Type Functional EquationsAddition and Subtraction TheoremsDifference Equations on SemigroupsMean-Value Type Functional EquationsApplications for Differential EquationsNoncommutative Applications Readership: Mathematicians, graduates and researchers in related fields. keywords:Functional Equations;Abelian Groups;Convolution;Exponentials;Exponential Polynomials;Mean Periodic Functions;Fourier Transform;Varieties;Spectral Analysis;Spectral Synthesis “The book yields a beautiful example of how the advanced methods of abstract harmonic analysis can be employed in the field of functional equations.” Mathematical Reviews
Functional Equations And Characterization Problems On Locally Compact Abelian Groups
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Author : Gennadiĭ Mikhaĭlovich Felʹdman
language : en
Publisher: European Mathematical Society
Release Date : 2008
Functional Equations And Characterization Problems On Locally Compact Abelian Groups written by Gennadiĭ Mikhaĭlovich Felʹdman and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Abelian groups categories.
This book deals with the characterization of probability distributions. It is well known that both the sum and the difference of two Gaussian independent random variables with equal variance are independent as well. The converse statement was proved independently by M. Kac and S. N. Bernstein. This result is a famous example of a characterization theorem. In general, characterization problems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions in these variables. In recent years, a great deal of attention has been focused upon generalizing the classical characterization theorems to random variables with values in various algebraic structures such as locally compact Abelian groups, Lie groups, quantum groups, or symmetric spaces. The present book is aimed at the generalization of some well-known characterization theorems to the case of independent random variables taking values in a locally compact Abelian group $X$. The main attention is paid to the characterization of the Gaussian and the idempotent distribution (group analogs of the Kac-Bernstein, Skitovich-Darmois, and Heyde theorems). The solution of the corresponding problems is reduced to the solution of some functional equations in the class of continuous positive definite functions defined on the character group of $X$. Group analogs of the Cramer and Marcinkiewicz theorems are also studied. The author is an expert in algebraic probability theory. His comprehensive and self-contained monograph is addressed to mathematicians working in probability theory on algebraic structures, abstract harmonic analysis, and functional equations. The book concludes with comments and unsolved problems that provide further stimulation for future research in the theory.
Regularity Properties Of Functional Equations In Several Variables
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Author : Antal Járai
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-03-03
Regularity Properties Of Functional Equations In Several Variables written by Antal Járai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-03 with Mathematics categories.
This book illustrates the basic ideas of regularity properties of functional equations by simple examples. It then treats most of the modern results about regularity of non-composite functional equations of several variables in a unified fashion. A long introduction highlights the basic ideas for beginners and several applications are also included.
Stability Of Functional Equations In Random Normed Spaces
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Author : Yeol Je Cho
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-27
Stability Of Functional Equations In Random Normed Spaces written by Yeol Je Cho and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-27 with Mathematics categories.
This book discusses the rapidly developing subject of mathematical analysis that deals primarily with stability of functional equations in generalized spaces. The fundamental problem in this subject was proposed by Stan M. Ulam in 1940 for approximate homomorphisms. The seminal work of Donald H. Hyers in 1941 and that of Themistocles M. Rassias in 1978 have provided a great deal of inspiration and guidance for mathematicians worldwide to investigate this extensive domain of research. The book presents a self-contained survey of recent and new results on topics including basic theory of random normed spaces and related spaces; stability theory for new function equations in random normed spaces via fixed point method, under both special and arbitrary t-norms; stability theory of well-known new functional equations in non-Archimedean random normed spaces; and applications in the class of fuzzy normed spaces. It contains valuable results on stability in random normed spaces, and is geared toward both graduate students and research mathematicians and engineers in a broad area of interdisciplinary research.
Functional Equations And Inequalities With Applications
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Author : Palaniappan Kannappan
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-10
Functional Equations And Inequalities With Applications written by Palaniappan Kannappan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-10 with Mathematics categories.
Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. This self-contained monograph explores all aspects of functional equations and their applications to related topics, such as differential equations, integral equations, the Laplace transformation, the calculus of finite differences, and many other basic tools in analysis. Each chapter examines a particular family of equations and gives an in-depth study of its applications as well as examples and exercises to support the material.
Functional Equations On Hypergroups
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Author : L szl¢ Szkelyhidi
language : en
Publisher: World Scientific
Release Date : 2013
Functional Equations On Hypergroups written by L szl¢ Szkelyhidi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
The theory of hypergroups is a rapidly developing area of mathematics due to its diverse applications in different areas like probability, harmonic analysis, etc. This book exhibits the use of functional equations and spectral synthesis in the theory of hypergroups. It also presents the fruitful consequences of this delicate OC marriageOCO where the methods of spectral analysis and synthesis can provide an efficient tool in characterization problems of function classes on hypergroups.This book is written for the interested reader who has open eyes for both functional equations and hypergroups, and who dares to enter a new world of ideas, a new world of methods OCo and, sometimes, a new world of unexpected difficulties.
Functional Equations On Hypergroups
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Author : László Székelyhidi
language : en
Publisher: World Scientific
Release Date : 2012-09-18
Functional Equations On Hypergroups written by László Székelyhidi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-18 with Mathematics categories.
The theory of hypergroups is a rapidly developing area of mathematics due to its diverse applications in different areas like probability, harmonic analysis, etc. This book exhibits the use of functional equations and spectral synthesis in the theory of hypergroups. It also presents the fruitful consequences of this delicate “marriage” where the methods of spectral analysis and synthesis can provide an efficient tool in characterization problems of function classes on hypergroups. This book is written for the interested reader who has open eyes for both functional equations and hypergroups, and who dares to enter a new world of ideas, a new world of methods — and, sometimes, a new world of unexpected difficulties. Contents:IntroductionPolynomial Hypergroups in One VariablePolynomial Hypergroups in Several VariablesSturm-Liouville HypergroupsTwo-Point Support HypergroupsSpectral Analysis and Synthesis on Polynomial HypergroupsSpectral Analysis and Synthesis on Sturm-Liouville HypergroupsMoment Problems on HypergroupsSpecial Functional Equations on HypergroupsDifference Equations on Polynomial HypergroupsStability Problems on Hypergroups Readership: Researchers and post-graduate students working in hypergroups. Keywords:Functional Equation;Hypergroup;Spectral SynthesisKey Features:The treatment applied here is completely new for those who are working in hypergroups: methods of functional equations and spectral synthesis have not been used beforeThis treatment also enriches the theory of functional equations: no classical functional equational methods have been applied before on structures like hypergroupsSeveral problems in both fields can be considered from a unique point of view of convolution type functional equationsReviews: “The author presents a new and very interesting idea of solving functional equations, which can stimulate mathematicians from different areas of mathematics to study and solve similar problems.” Zentralblatt MATH
Inequalities And Applications
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Author : Catherine Bandle
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-17
Inequalities And Applications written by Catherine Bandle and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-17 with Mathematics categories.
Inequalities continue to play an essential role in mathematics. Perhaps, they form the last field comprehended and used by mathematicians in all areas of the discipline. Since the seminal work Inequalities (1934) by Hardy, Littlewood and Pólya, mathematicians have laboured to extend and sharpen their classical inequalities. New inequalities are discovered every year, some for their intrinsic interest whilst others flow from results obtained in various branches of mathematics. The study of inequalities reflects the many and various aspects of mathematics. On one hand, there is the systematic search for the basic principles and the study of inequalities for their own sake. On the other hand, the subject is the source of ingenious ideas and methods that give rise to seemingly elementary but nevertheless serious and challenging problems. There are numerous applications in a wide variety of fields, from mathematical physics to biology and economics. This volume contains the contributions of the participants of the Conference on Inequalities and Applications held in Noszvaj (Hungary) in September 2007. It is conceived in the spirit of the preceding volumes of the General Inequalities meetings held in Oberwolfach from 1976 to 1995 in the sense that it not only contains the latest results presented by the participants, but it is also a useful reference book for both lecturers and research workers. The contributions reflect the ramification of general inequalities into many areas of mathematics and also present a synthesis of results in both theory and practice.
Inner Product Spaces And Applications
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Author : T M Rassias
language : en
Publisher: CRC Press
Release Date : 1997-10-08
Inner Product Spaces And Applications written by T M Rassias and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-08 with Mathematics categories.
In this volume, the contributing authors deal primarily with the interaction among problems of analysis and geometry in the context of inner product spaces. They present new and old characterizations of inner product spaces among normed linear spaces and the use of such spaces in various research problems of pure and applied mathematics. The methods employed are accessible to students familiar with normed linear spaces. Some of the theorems presented are at the same time simple and challenging.