Spaces Of Fundamental And Generalized Function

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Spaces Of Fundamental And Generalized Function

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Author : Izrailʹ Moiseevič Gelʹfand (Mathématicien)
language : en
Publisher:
Release Date : 1968

Spaces Of Fundamental And Generalized Function written by Izrailʹ Moiseevič Gelʹfand (Mathématicien) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.

Generalized Functions

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Author :
language : en
Publisher:
Release Date : 1972

Generalized Functions written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with categories.

Spaces Of Fundamental And Generalized Functions

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Author : Izrailʹ Moiseevich Gelʹfand
language : en
Publisher:
Release Date : 1968

Spaces Of Fundamental And Generalized Functions written by Izrailʹ Moiseevich Gelʹfand and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Functions categories.

Generalized Functions Theory And Technique

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Author : Ram P. Kanwal
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-01-01

Generalized Functions Theory And Technique written by Ram P. Kanwal 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 1998-01-01 with Mathematics categories.

This second edition of Generalized Functions has been strengthened in many ways. The already extensive set of examples has been expanded. Since the publication of the first edition, there has been tremendous growth in the subject and I have attempted to incorporate some of these new concepts. Accordingly, almost all the chapters have been revised. The bibliography has been enlarged considerably. Some of the material has been reorganized. For example, Chapters 12 and 13 of the first edition have been consolidated into Chapter 12 of this edition by a judicious process of elimination and addition of the subject matter. The new Chapter 13 explains the interplay between the theories of moments, asymptotics, and singular perturbations. Similarly, some sections of Chapter 15 have been revised and included in earlier chapters to improve the logical flow of ideas. However, two sections are retained. The section dealing with the application of the probability theory has been revised, and I am thankful to Professor Z.L. Crvenkovic for her help. The new material included in this chapter pertains to the modern topics of periodic distributions and microlocal theory. I have demonstrated through various examples that familiarity with the generalized functions is very helpful for students in physical sciences and technology. For instance, the reader will realize from Chapter 6 how the generalized functions have revolutionized the Fourier analysis which is being used extensively in many fields of scientific activity.

Generalized Functions Volume 2

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Author : I. M. Gel'fand
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-03-30

Generalized Functions Volume 2 written by I. M. Gel'fand and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-30 with Mathematics categories.

The first systematic theory of generalized functions (also known as distributions) was created in the early 1950s, although some aspects were developed much earlier, most notably in the definition of the Green's function in mathematics and in the work of Paul Dirac on quantum electrodynamics in physics. The six-volume collection, Generalized Functions, written by I. M. Gel'fand and co-authors and published in Russian between 1958 and 1966, gives an introduction to generalized functions and presents various applications to analysis, PDE, stochastic processes, and representation theory. Volume 2 is devoted to detailed study of generalized functions as linear functionals on appropriate spaces of smooth test functions. In Chapter 1, the authors introduce and study countable-normed linear topological spaces, laying out a general theoretical foundation for the analysis of spaces of generalized functions. The two most important classes of spaces of test functions are spaces of compactly supported functions and Schwartz spaces of rapidly decreasing functions. In Chapters 2 and 3 of the book, the authors transfer many results presented in Volume 1 to generalized functions corresponding to these more general spaces. Finally, Chapter 4 is devoted to the study of the Fourier transform; in particular, it includes appropriate versions of the Paley-Wiener theorem.

Orlicz Spaces And Generalized Orlicz Spaces

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Author : Petteri Harjulehto
language : en
Publisher: Springer
Release Date : 2019-05-07

Orlicz Spaces And Generalized Orlicz Spaces written by Petteri Harjulehto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.

This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–Poincaré inequalities in norm and modular forms. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.

Spaces Of Fundamental And Generalized Functions

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Author : I. M. Gel'Fand
language : en
Publisher: Academic Press
Release Date : 2013-09-03

Spaces Of Fundamental And Generalized Functions written by I. M. Gel'Fand and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-03 with Mathematics categories.

Spaces of Fundamental and Generalized Functions, Volume 2, analyzes the general theory of linear topological spaces. The basis of the theory of generalized functions is the theory of the so-called countably normed spaces (with compatible norms), their unions (inductive limits), and also of the spaces conjugate to the countably normed ones or their unions. This set of spaces is sufficiently broad on the one hand, and sufficiently convenient for the analyst on the other. The book opens with a chapter that discusses the theory of these spaces. This is followed by separate chapters on fundamental and generalized functions, Fourier transformations of fundamental and generalized functions, and spaces of type S.

Generalized Functions And Fourier Analysis

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Author : Michael Oberguggenberger
language : en
Publisher: Birkhäuser
Release Date : 2017-05-06

Generalized Functions And Fourier Analysis written by Michael Oberguggenberger and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-06 with Mathematics categories.

This book gives an excellent and up-to-date overview on the convergence and joint progress in the fields of Generalized Functions and Fourier Analysis, notably in the core disciplines of pseudodifferential operators, microlocal analysis and time-frequency analysis. The volume is a collection of chapters addressing these fields, their interaction, their unifying concepts and their applications and is based on scientific activities related to the International Association for Generalized Functions (IAGF) and the ISAAC interest groups on Pseudo-Differential Operators (IGPDO) and on Generalized Functions (IGGF), notably on the longstanding collaboration of these groups within ISAAC.

Generalized Functions Spaces Of Fundamental And Generalized Functions

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Author : Izrailʹ Moiseevich Gelʹfand
language : en
Publisher:
Release Date : 2016

Generalized Functions Spaces Of Fundamental And Generalized Functions written by Izrailʹ Moiseevich Gelʹfand and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Theory of distributions (Functional analysis) categories.

Generalized Functions

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Author : Izrailʹ Moiseevich Gelʹfand
language : en
Publisher:
Release Date : 1968

Generalized Functions written by Izrailʹ Moiseevich Gelʹfand and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Differential equations categories.