Convolution Type Functional Equations On Topological Abelian Groups

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Convolution Type Functional Equations on Topological Abelian Groups

Author : L szl¢ Szkelyhidi
Publisher : World Scientific
ISBN 13 : 9789810206581
Total Pages : 180 pages
Book Rating : 4.2/5 (65 download)

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Book Synopsis Convolution Type Functional Equations on Topological Abelian Groups by : L szl¢ Szkelyhidi

Download or read book Convolution Type Functional Equations on Topological Abelian Groups written by L szl¢ Szkelyhidi and published by World Scientific. This book was released on 1991 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : László Székelyhidi
Publisher : World Scientific
ISBN 13 : 9814506206
Total Pages : 172 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Convolution Type Functional Equations on Topological Abelian Groups by : László Székelyhidi

Download or read book Convolution Type Functional Equations on Topological Abelian Groups written by László Székelyhidi and published by World Scientific. This book was released on 1991-04-22 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Gennadiĭ Mikhaĭlovich Felʹdman
Publisher : European Mathematical Society
ISBN 13 : 9783037190456
Total Pages : 272 pages
Book Rating : 4.1/5 (94 download)

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Book Synopsis Functional Equations and Characterization Problems on Locally Compact Abelian Groups by : Gennadiĭ Mikhaĭlovich Felʹdman

Download or read book Functional Equations and Characterization Problems on Locally Compact Abelian Groups written by Gennadiĭ Mikhaĭlovich Felʹdman and published by European Mathematical Society. This book was released on 2008 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Functional Equations and Inequalities with Applications

Author : Palaniappan Kannappan
Publisher : Springer Science & Business Media
ISBN 13 : 0387894926
Total Pages : 817 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Functional Equations and Inequalities with Applications by : Palaniappan Kannappan

Download or read book Functional Equations and Inequalities with Applications written by Palaniappan Kannappan and published by Springer Science & Business Media. This book was released on 2009-06-10 with total page 817 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Regularity Properties of Functional Equations in Several Variables

Author : Antal Járai
Publisher : Springer Science & Business Media
ISBN 13 : 9780387244136
Total Pages : 378 pages
Book Rating : 4.2/5 (441 download)

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Book Synopsis Regularity Properties of Functional Equations in Several Variables by : Antal Járai

Download or read book Regularity Properties of Functional Equations in Several Variables written by Antal Járai and published by Springer Science & Business Media. This book was released on 2005-03-03 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Yeol Je Cho
Publisher : Springer Science & Business Media
ISBN 13 : 1461484774
Total Pages : 255 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Stability of Functional Equations in Random Normed Spaces by : Yeol Je Cho

Download or read book Stability of Functional Equations in Random Normed Spaces written by Yeol Je Cho and published by Springer Science & Business Media. This book was released on 2013-08-27 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 on Hypergroups

Author : L szl¢ Szkelyhidi
Publisher : World Scientific
ISBN 13 : 9814407011
Total Pages : 210 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Functional Equations on Hypergroups by : L szl¢ Szkelyhidi

Download or read book Functional Equations on Hypergroups written by L szl¢ Szkelyhidi and published by World Scientific. This book was released on 2013 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : László Székelyhidi
Publisher : World Scientific
ISBN 13 : 981440702X
Total Pages : 212 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Functional Equations on Hypergroups by : László Székelyhidi

Download or read book Functional Equations on Hypergroups written by László Székelyhidi and published by World Scientific. This book was released on 2012-09-18 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Inner Product Spaces and Applications

Author : T M Rassias
Publisher : CRC Press
ISBN 13 : 9780582317116
Total Pages : 284 pages
Book Rating : 4.3/5 (171 download)

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Book Synopsis Inner Product Spaces and Applications by : T M Rassias

Download or read book Inner Product Spaces and Applications written by T M Rassias and published by CRC Press. This book was released on 1997-10-08 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization

Author : Said Melliani
Publisher : Springer Nature
ISBN 13 : 3031124162
Total Pages : 496 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization by : Said Melliani

Download or read book Recent Advances in Fuzzy Sets Theory, Fractional Calculus, Dynamic Systems and Optimization written by Said Melliani and published by Springer Nature. This book was released on 2022-08-10 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe in this book recent advances in fuzzy sets theory, fractional calculus, dynamic systems, and optimization. The book provides a setting for the discussion of recent developments in a wide variety of topics including partial differential equations, dynamic systems, optimization, numerical analysis, fuzzy sets theory, fractional calculus, and its applications. The book is aimed at bringing together contributions from leading academic scientists, researchers, and research scholars to exchange and share their experiences and research results on all aspects of applied mathematics, modeling, algebra, economics, finance, and applications. It also provides an interdisciplinary platform for researchers, practitioners, and educators to present the most recent innovations, trends, and concerns as well as practical challenges encountered and solutions adopted in the fields of applied mathematics. The published chapters address various aspects of academic scientists, researchers, and research scholars in many variety mathematical topics.

Inequalities and Applications

Author : Catherine Bandle
Publisher : Springer Science & Business Media
ISBN 13 : 3764387734
Total Pages : 330 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Inequalities and Applications by : Catherine Bandle

Download or read book Inequalities and Applications written by Catherine Bandle and published by Springer Science & Business Media. This book was released on 2008-12-17 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Analysis

Author : Panos M. Pardalos
Publisher : Springer Science & Business Media
ISBN 13 : 146143498X
Total Pages : 898 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Nonlinear Analysis by : Panos M. Pardalos

Download or read book Nonlinear Analysis written by Panos M. Pardalos and published by Springer Science & Business Media. This book was released on 2012-06-02 with total page 898 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume will consist of about 40 articles written by some very influential mathematicians of our time and will expose the latest achievements in the broad area of nonlinear analysis and its various interdisciplinary applications.

Inequalities and Applications

Author : Ravi P. Agarwal
Publisher : World Scientific
ISBN 13 : 9789810218300
Total Pages : 568 pages
Book Rating : 4.2/5 (183 download)

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Book Synopsis Inequalities and Applications by : Ravi P. Agarwal

Download or read book Inequalities and Applications written by Ravi P. Agarwal and published by World Scientific. This book was released on 1994 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: World Scientific Series in Applicable Analysis (WSSIAA) reports new developments of a high mathematical standard and of current interest. Each volume in the series is devoted to mathematical analysis that has been applied, or is potentially applicable to the solution of scientific, engineering, and social problems. The third volume of WSSIAA contains 47 research articles on inequalities by leading mathematicians from all over the world and a tribute by R.M. Redheffer to Wolfgang Walter ? to whom this volume is dedicated ? on his 66th birthday.Contributors: A Acker, J D Aczl, A Alvino, K A Ames, Y Avishai, C Bandle, B M Brown, R C Brown, D Brydak, P S Bullen, K Deimling, J Diaz, ? Elbert, P W Eloe, L H Erbe, H Esser, M Essn, W D Evans, W N Everitt, V Ferone, A M Fink, R Ger, R Girgensohn, P Goetgheluck, W Haussmann, S Heikkil, J Henderson, G Herzog, D B Hinton, T Horiuchi, S Hu, B Kawohl, V G Kirby; N Kirchhoff, G H Knightly, H W Knobloch, Q Kong, H Knig, A Kufner, M K Kwong, A Laforgia, V Lakshmikantham, S Leela, R Lemmert, E R Love, G Lttgens, S Malek, R Man sevich, J Mawhin, R Medina, M Migda, R J Nessel, Z P les, N S Papageorgiou, L E Payne, J Pe?ari, L E Persson, A Peterson, M Pinto, M Plum, J Popenda, G Porru, R M Redheffer, A A Sagle, S Saitoh, D Sather, K Schmitt, D F Shea, A Simon, S Sivasundaram, R Sperb, C S Stanton, G Talenti, G Trombetti, S Varo?anec, A S Vatsala, P Volkmann, H Wang, V Weckesser, F Zanolin, K Zeller, A Zettl.

Operator Relations Characterizing Derivatives

Author : Hermann König
Publisher : Springer
ISBN 13 : 3030002411
Total Pages : 191 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Operator Relations Characterizing Derivatives by : Hermann König

Download or read book Operator Relations Characterizing Derivatives written by Hermann König and published by Springer. This book was released on 2018-10-03 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops an operator viewpoint for functional equations in classical function spaces of analysis, thus filling a void in the mathematical literature. Major constructions or operations in analysis are often characterized by some elementary properties, relations or equations which they satisfy. The authors present recent results on the problem to what extent the derivative is characterized by equations such as the Leibniz rule or the Chain rule operator equation in Ck-spaces. By localization, these operator equations turn into specific functional equations which the authors then solve. The second derivative, Sturm-Liouville operators and the Laplacian motivate the study of certain "second-order" operator equations. Additionally, the authors determine the general solution of these operator equations under weak assumptions of non-degeneration. In their approach, operators are not required to be linear, and the authors also try to avoid continuity conditions. The Leibniz rule, the Chain rule and its extensions turn out to be stable under perturbations and relaxations of assumptions on the form of the operators. The results yield an algebraic understanding of first- and second-order differential operators. Because the authors have chosen to characterize the derivative by algebraic relations, the rich operator-type structure behind the fundamental notion of the derivative and its relatives in analysis is discovered and explored. The book does not require any specific knowledge of functional equations. All needed results are presented and proven and the book is addressed to a general mathematical audience.

Mathematical Analysis and Applications

Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414342
Total Pages : 764 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-05-11 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.

Functional Equations On Groups

Author : Henrik Stetkaer
Publisher : World Scientific
ISBN 13 : 9814513148
Total Pages : 396 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Functional Equations On Groups by : Henrik Stetkaer

Download or read book Functional Equations On Groups written by Henrik Stetkaer and published by World Scientific. This book was released on 2013-07-15 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an accessible and coherent introduction to some of the scientific progress on functional equations on groups in the last two decades. It presents the latest methods of treating the topic and contains new and transparent proofs. Its scope extends from the classical functional equations on the real line to those on groups, in particular, non-abelian groups. This volume presents, in careful detail, a number of illustrative examples like the cosine equation on the Heisenberg group and on the group SL(2, ℝ). Some of the examples are not even seen in existing monographs. Thus, it is an essential source of reference for further investigations.

Harmonic And Spectral Analysis

Author : Laszlo Szekelyhidi
Publisher : World Scientific
ISBN 13 : 9814531731
Total Pages : 248 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Harmonic And Spectral Analysis by : Laszlo Szekelyhidi

Download or read book Harmonic And Spectral Analysis written by Laszlo Szekelyhidi and published by World Scientific. This book was released on 2014-03-19 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a modern introduction to harmonic analysis and synthesis on topological groups. It serves as a guide to the abstract theory of Fourier transformation. For the first time, it presents a detailed account of the theory of classical harmonic analysis together with the recent developments in spectral analysis and synthesis.