generalized functions volume 4 applications of harmonic analysis ams chelsea publishing

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Generalized Functions Volume 4

Author : I. M. Gel′fand
ISBN : 1470431254
Genre : Theory of distributions (Functional analysis)
File Size : 49. 49 MB
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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. Gel2 and 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. The main.

Generalized Functions Applications Of Harmonic Analysis

Author : Izrailʹ Moiseevich Gelʹfand
ISBN : LCCN:2015040021
Genre : Theory of distributions (Functional analysis)
File Size : 27. 98 MB
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Ultrametric Pseudodifferential Equations And Applications

Author : Andrei Yu. Khrennikov
ISBN : 9781108102902
Genre : Mathematics
File Size : 69. 29 MB
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Starting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows the ways in which these equations link different fields including mathematics, engineering, and geophysics. In particular, the authors provide a detailed explanation of the geophysical applications of p-adic diffusion equations, useful when modeling the flows of liquids through porous rock. p-adic wavelets theory and p-adic pseudodifferential equations are also presented, along with their connections to mathematical physics, representation theory, the physics of disordered systems, probability, number theory, and p-adic dynamical systems. Material that was previously spread across many articles in journals of many different fields is brought together here, including recent work on the van der Put series technique. This book provides an excellent snapshot of the fascinating field of ultrametric pseudodifferential equations, including their emerging applications and currently unsolved problems.

Generalized Functions

Author : Izrailʹ Moiseevich Gelʹfand
ISBN : 0122795059
Genre : Theory of distributions (Functional analysis)
File Size : 41. 1 MB
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Generalized Functions Volume 2

Author : I. M. Gel'fand
ISBN : 9781470426590
Genre : Theory of distributions (Functional analysis)
File Size : 45. 32 MB
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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.

Pseudo Differential Operators And Generalized Functions

Author : Stevan Pilipović
ISBN : 9783319146188
Genre : Mathematics
File Size : 81. 31 MB
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This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators. It is dedicated to Professor Michael Oberguggenberger (Innsbruck University, Austria) in honour of his 60th birthday. The topics covered were suggested by the ISAAC Group in Generalized Functions (GF) and the ISAAC Group in Pseudo-Differential Operators (IGPDO), which met at the 9th ISAAC congress in Krakow, Poland in August 2013. Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis. Featuring both essays and research articles, the book will be of great interest to graduate students and researchers working in analysis, PDE and mathematical physics, while also offering a valuable complement to the volumes on this topic previously published in the OT series.

Generalized Functions Volume 1

Author : I. M. Gel′fand
ISBN : 9781470426583
Genre : Theory of distributions (Functional analysis)
File Size : 62. 66 MB
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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.

Generalized Functions Theory Of Differential Equations By I M Gel Fand And G E Shilov

Author : Izrailʹ Moiseevich Gelʹfand
ISBN : UOM:49015002024413
Genre : Functional analysis
File Size : 86. 89 MB
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Siam Journal On Control And Optimization

Author :
ISBN : UCSD:31822033939026
Genre : Control theory
File Size : 51. 59 MB
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Technical Book Review

Author :
ISBN : UCAL:$B619147
Genre : Books
File Size : 45. 54 MB
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