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Author: Nikolaĭ Nikolaevich Bogoli︠u︡bov
Publisher:
ISBN:
Category : Functions of complex variables
Languages : en
Pages : 74
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Book Description
Author: Nikolaĭ Nikolaevich Bogoli︠u︡bov
Publisher:
ISBN:
Category : Functions of complex variables
Languages : en
Pages : 74
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Book Description
Author: I. M. Gel′fand
Publisher: American Mathematical Soc.
ISBN: 1470426587
Category : Mathematics
Languages : en
Pages : 450
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Book Description
he 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 1 is devoted to basics of the theory of generalized functions. The first chapter contains main definitions and most important properties of generalized functions as functional on the space of smooth functions with compact support. The second chapter talks about the Fourier transform of generalized functions. In Chapter 3, definitions and properties of some important classes of generalized functions are discussed; in particular, generalized functions supported on submanifolds of lower dimension, generalized functions associated with quadratic forms, and homogeneous generalized functions are studied in detail. Many simple basic examples make this book an excellent place for a novice to get acquainted with the theory of generalized functions. A long appendix presents basics of generalized functions of complex variables.
Author: Nikolaĭ Nikolaevich Bogoli︠u︡bov
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 64
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Book Description
Author: J. F. Colombeau
Publisher:
ISBN:
Category :
Languages : en
Pages : 8
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Book Description
Author: I. M. Gel'fand
Publisher: Academic Press
ISBN: 148326159X
Category : Mathematics
Languages : en
Pages : 442
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Book Description
Generalized Functions, Volume 1: Properties and Operations provides a systematic development of the theory of generalized functions and problems in analysis connected with it. This book focuses on the concept of a convenient link that connects many aspects of analysis, functional analysis, theory of differential equations, representation theory of locally compact Lie groups, and theory of probability and statistics. This volume is essentially devoted to algorithmic questions of the theory, covering many applications of generalized functions to various problems of analysis. The topics discussed include the local properties of generalized functions, differentiation as a continuous operation, and Fourier Transforms of test functions. The wave equation in space of odd dimension, derivation of Green's theorem, and reducible singular points are also described. This publication is a good reference for mathematicians, researchers, and students concerned with generalized functions.
Author: Ram P. Kanwal
Publisher: Springer Science & Business Media
ISBN: 9780817640064
Category : Mathematics
Languages : en
Pages : 478
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Book Description
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.
Author: O.P. Misra
Publisher: Elsevier
ISBN: 0080872301
Category : Mathematics
Languages : en
Pages : 347
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Book Description
Transform Analysis of Generalized Functions concentrates on finite parts of integrals, generalized functions and distributions. It gives a unified treatment of the distributional setting with transform analysis, i.e. Fourier, Laplace, Stieltjes, Mellin, Hankel and Bessel Series.Included are accounts of applications of the theory of integral transforms in a distributional setting to the solution of problems arising in mathematical physics. Information on distributional solutions of differential, partial differential equations and integral equations is conveniently collected here.The volume will serve as introductory and reference material for those interested in analysis, applications, physics and engineering.
Author: William T. Ross
Publisher: American Mathematical Soc.
ISBN: 0821831755
Category : Mathematics
Languages : en
Pages : 165
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Book Description
The theory of generalized analytic continuation studies continuations of meromorphic functions in situations where traditional theory says there is a natural boundary. This broader theory touches on a remarkable array of topics in classical analysis, as described in the book. The authors use the strong analogy with the summability of divergent series to motivate the subject. They are careful to cover the various types of continuations, attempting to unify them and suggesting some open questions. The book also addresses the role of such continuations in approximation theory and operator theory. The introductory overview provides a useful look at the history and context of the theory.
Author: Izrailʹ Moiseevich Gelʹfand
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 454
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Book Description
Author: Kanwal
Publisher: Academic Press
ISBN: 0080956769
Category : Computers
Languages : en
Pages : 443
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Book Description
Generalized Functions: Theory and Technique
