The Cauchy Problem For Convolution Equations
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Tube Domains And The Cauchy Problem
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Author : Semen Grigorʹevich Gindikin
language : en
Publisher: American Mathematical Soc.
Release Date :
Tube Domains And The Cauchy Problem written by Semen Grigorʹevich Gindikin 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 with Mathematics categories.
This book is dedicated to two problems. The first concerns the description of maximal exponential growth of functions or distributions for which the Cauchy problem is well posed. The descriptions presented in the language of the behaviour of the symbol in a complex domain. The second problem concerns the structure of and explicit formulas for differential operators with large automorphism groups. It is suitable as an advanced graduate text in courses in partial differential equations and the theory of distributions.
The Cauchy Problem For Convolution Equations
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Author : Leonid Romanovich Volevich
language : en
Publisher:
Release Date : 1994
The Cauchy Problem For Convolution Equations written by Leonid Romanovich Volevich and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Cauchy problem categories.
The Cauchy Problem
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Author : Hector O. Fattorini
language : en
Publisher: Cambridge University Press
Release Date : 1983
The Cauchy Problem written by Hector O. Fattorini and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students.
Stochastic Cauchy Problems In Infinite Dimensions
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Author : Irina V. Melnikova
language : en
Publisher: CRC Press
Release Date : 2018-09-03
Stochastic Cauchy Problems In Infinite Dimensions written by Irina V. Melnikova and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.
Stochastic Cauchy Problems in Infinite Dimensions: Generalized and Regularized Solutions presents stochastic differential equations for random processes with values in Hilbert spaces. Accessible to non-specialists, the book explores how modern semi-group and distribution methods relate to the methods of infinite-dimensional stochastic analysis. It also shows how the idea of regularization in a broad sense pervades all these methods and is useful for numerical realization and applications of the theory. The book presents generalized solutions to the Cauchy problem in its initial form with white noise processes in spaces of distributions. It also covers the "classical" approach to stochastic problems involving the solution of corresponding integral equations. The first part of the text gives a self-contained introduction to modern semi-group and abstract distribution methods for solving the homogeneous (deterministic) Cauchy problem. In the second part, the author solves stochastic problems using semi-group and distribution methods as well as the methods of infinite-dimensional stochastic analysis.
Distributions And Convolution Equations
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Author : Semen Grigorʹevich Gindikin
language : en
Publisher: CRC Press
Release Date : 1992
Distributions And Convolution Equations written by Semen Grigorʹevich Gindikin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
The authors apply the results of many years of their own original research to a systematic presentation of the theory of distributions in this monograph which can also be used as a (very expensive) textbook on the theory of distribution for graduate students. The first part is devoted to the Cauchy problem, while the second part deals with the Wiener-Hopf equation and related topics in the theory of boundary value problems for convolution equations. To make their work more accessible to readers new to this field, the authors restrict initial treatment of problems to the half-line and formulate only principal results, in their simplest form. Special results and possible generalizations are presented as problems and exercises. Annotation copyrighted by Book News, Inc., Portland, OR
Transactions Of The Moscow Mathematical Society
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Author : P. S. Aleksandrov
language : en
Publisher: American Mathematical Soc.
Release Date : 1976-12-31
Transactions Of The Moscow Mathematical Society written by P. S. Aleksandrov 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 1976-12-31 with Mathematics categories.
Focuses on topics in differential equations, including linear partialdifferential equations, elliptic equations, pseudodifferential equations, and Petrovskii-correct differential operators. This volume is dedicated to the memory of Ivan Georgievic Petrovskii and contains a memoriam of his life and work
The Mathematics Of Superoscillations
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Author : Yakir Aharonov
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-04-25
The Mathematics Of Superoscillations written by Yakir Aharonov 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 2017-04-25 with Mathematics categories.
In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed that superoscillations naturally arise when dealing with weak values, a notion that provides a fundamentally different way to regard measurements in quantum physics. From a mathematical point of view, superoscillating functions are a superposition of small Fourier components with a bounded Fourier spectrum, which result, when appropriately summed, in a shift that can be arbitrarily large, and well outside the spectrum. The purpose of this work is twofold: on one hand the authors provide a self-contained survey of the existing literature, in order to offer a systematic mathematical approach to superoscillations; on the other hand, they obtain some new and unexpected results, by showing that superoscillating sequences can be seen of as solutions to a large class of convolution equations and can therefore be treated within the theory of analytically uniform spaces. In particular, the authors will also discuss the persistence of the superoscillatory behavior when superoscillating sequences are taken as initial values of the Schrödinger equation and other equations.
Convolution Like Structures Differential Operators And Diffusion Processes
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Author : Rúben Sousa
language : en
Publisher: Springer Nature
Release Date : 2022-07-27
Convolution Like Structures Differential Operators And Diffusion Processes written by Rúben Sousa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-27 with Mathematics categories.
This book provides an introduction to recent developments in the theory of generalized harmonic analysis and its applications. It is well known that convolutions, differential operators and diffusion processes are interconnected: the ordinary convolution commutes with the Laplacian, and the law of Brownian motion has a convolution semigroup property with respect to the ordinary convolution. Seeking to generalize this useful connection, and also motivated by its probabilistic applications, the book focuses on the following question: given a diffusion process Xt on a metric space E, can we construct a convolution-like operator * on the space of probability measures on E with respect to which the law of Xt has the *-convolution semigroup property? A detailed analysis highlights the connection between the construction of convolution-like structures and disciplines such as stochastic processes, ordinary and partial differential equations, spectral theory, special functions and integral transforms. The book will be valuable for graduate students and researchers interested in the intersections between harmonic analysis, probability theory and differential equations.
Special Functions And Analysis Of Differential Equations
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Author : Praveen Agarwal
language : en
Publisher: CRC Press
Release Date : 2020-09-08
Special Functions And Analysis Of Differential Equations written by Praveen Agarwal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-08 with Mathematics categories.
Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.
Generalized Functions And Partial Differential Equations
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Author : Avner Friedman
language : en
Publisher: Courier Corporation
Release Date : 2005-12-10
Generalized Functions And Partial Differential Equations written by Avner Friedman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-10 with Mathematics categories.
This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to solving a variety of problems in partial differential equations. A major portion of the text is based on material included in the books of L. Schwartz, who developed the theory of distributions, and in the books of Gelfand and Shilov, who deal with generalized functions of any class and their use in solving the Cauchy problem. In addition, the author provides applications developed through his own research. Geared toward upper-level undergraduates and graduate students, the text assumes a sound knowledge of both real and complex variables. Familiarity with the basic theory of functional analysis, especially normed spaces, is helpful but not necessary. An introductory chapter features helpful background on topological spaces. Applications to partial differential equations include a treatment of the Cauchy problem, the Goursat problem, fundamental solutions, existence and differentiality of solutions of equations with constants, coefficients, and related topics. Supplementary materials include end-of-chapter problems, bibliographical remarks, and a bibliography.