Tauberian Theorems For Generalized Functions

Author : V.S. Vladimirov,Yu.N. Drozzinov,O.I. Zavialov
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400928312

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Tauberian Theorems for Generalized Functions by V.S. Vladimirov,Yu.N. Drozzinov,O.I. Zavialov Pdf

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. The Scandal of Father G. K. Chesterton. 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Author : V S Vladimirov,Yu N Drozzinov,O I Zavialov
Publisher : Unknown
Page : 312 pages
File Size : 45,8 Mb
Release : 1988-04-30
Category : Electronic
ISBN : 9400928327

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Tauberian Theorems for Generalized Functions by V S Vladimirov,Yu N Drozzinov,O I Zavialov Pdf

Author : Stevan Pilipovi?,Bogoljub Stankovi?,Jasson Vindas
Publisher : World Scientific
Page : 309 pages
File Size : 52,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814366847

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Asymptotic Behavior of Generalized Functions by Stevan Pilipovi?,Bogoljub Stankovi?,Jasson Vindas Pdf

The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach ? of Estrada, Kanwal and Vindas ? is related to moment asymptotic expansions of generalized functions and the Ces'aro behavior. The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. The book can be used by applied mathematicians, physicists, engineers and others who use classical asymptotic methods and wish to consider non-classical objects (generalized functions) and their asymptotics now in a more advanced setting.

Author : V. S. Vladimirov
Publisher : CRC Press
Page : 332 pages
File Size : 51,9 Mb
Release : 2002-08-15
Category : Mathematics
ISBN : 0415273560

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Methods of the Theory of Generalized Functions by V. S. Vladimirov Pdf

This volume presents the general theory of generalized functions, including the Fourier, Laplace, Mellin, Hilbert, Cauchy-Bochner and Poisson integral transforms and operational calculus, with the traditional material augmented by the theory of Fourier series, abelian theorems, and boundary values of helomorphic functions for one and several variables. The author addresses several facets in depth, including convolution theory, convolution algebras and convolution equations in them, homogenous generalized functions, and multiplication of generalized functions. This book will meet the needs of researchers, engineers, and students of applied mathematics, control theory, and the engineering sciences.

Author : Stevan Pilipović,Joachim Toft
Publisher : Birkhäuser
Page : 290 pages
File Size : 42,6 Mb
Release : 2015-04-27
Category : Mathematics
ISBN : 9783319146188

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Pseudo-Differential Operators and Generalized Functions by Stevan Pilipović,Joachim Toft Pdf

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.

Author : Stevan Pilipovic,Bogoljub Stankovic,Jasson Vindas
Publisher : World Scientific
Page : 309 pages
File Size : 48,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814366854

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Asymptotic Behavior of Generalized Functions by Stevan Pilipovic,Bogoljub Stankovic,Jasson Vindas Pdf

The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach OCo of Estrada, Kanwal and Vindas OCo is related to moment asymptotic expansions of generalized functions and the Ces''aro behavior. The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. The book can be used by applied mathematicians, physicists, engineers and others who use classical asymptotic methods and wish to consider non-classical objects (generalized functions) and their asymptotics now in a more advanced setting.

Author : Brychkov
Publisher : CRC Press
Page : 362 pages
File Size : 49,9 Mb
Release : 1989-04-20
Category : Mathematics
ISBN : 2881247059

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Integral Transforms of Generalized Functions by Brychkov Pdf

English translation (from revised and enlarged versions of the Russian editions of 1977 and 1984) of a reference work which makes available to engineers, physicists and applied mathematicians theoretical and tabular material pertaining to certain extensions of standard integral transform techniques. Diverse transforms are touched upon, but the emphasis (particularly in the tables) is on generalized Fourier and Laplace transforms. Some multi-dimensional results are presented. Expensive, but nicely produced, and redundant with nothing standard to the reference shelves of mathematical libraries. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

Author : Arsen L. Yakimiv
Publisher : Walter de Gruyter
Page : 236 pages
File Size : 43,9 Mb
Release : 2012-03-20
Category : Mathematics
ISBN : 9783110195293

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Probabilistic Applications of Tauberian Theorems by Arsen L. Yakimiv Pdf

The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.

Author : Vasiliĭ Sergeevich Vladimirov,Evgeniĭ Frolovich Mishchenko,A. K. Gushchin
Publisher : American Mathematical Soc.
Page : 270 pages
File Size : 49,8 Mb
Release : 1988
Category : Mathematics
ISBN : 0821831194

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Theoretical and Mathematical Physics by Vasiliĭ Sergeevich Vladimirov,Evgeniĭ Frolovich Mishchenko,A. K. Gushchin Pdf

Author : Bogoljub Stankovic
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461310556

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Generalized Functions, Convergence Structures, and Their Applications by Bogoljub Stankovic Pdf

This Proceedings consists of a collection of papers presented at the International Conference "Generalized functions, convergence structures and their applications" held from June 23-27, 1987 in Dubrovnik, Yugoslavia (GFCA-87): 71 participants from 21 countr~es from allover the world took part in the Conference. Proceedings reflects the work of the Conference. Plenary lectures of J. Burzyk, J. F. Colombeau, W. Gahler, H. Keiter, H. Komatsu, B. Stankovic, H. G. Tillman, V. S. Vladimirov provide an up-to-date account of the cur rent state of the subject. All these lectures, except H. G. Tillman's, are published in this volume. The published communications give the contemporary problems and achievements in the theory of generalized functions, in the theory of convergence structures and in their applications, specially in the theory of partial differential equations and in the mathematical physics. New approaches to the theory of generalized functions are presented, moti vated by concrete problems of applications. The presence of articles of experts in mathematical physics contributed to this aim. At the end of the volume one can find presented open problems which also point to further course of development in the theory of generalized functions and convergence structures. We are very grateful to Mr. Milan Manojlovic who typed these Proce edings with extreme skill and diligence and with inexhaustible patience.

Author : Shahla Molahajloo,Stevan Pilipović,Joachim Toft,M. W. Wong
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 44,6 Mb
Release : 2013-02-26
Category : Mathematics
ISBN : 9783034805858

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Pseudo-Differential Operators, Generalized Functions and Asymptotics by Shahla Molahajloo,Stevan Pilipović,Joachim Toft,M. W. Wong Pdf

This volume consists of twenty peer-reviewed papers from the special session on pseudodifferential operators and the special session on generalized functions and asymptotics at the Eighth Congress of ISAAC held at the Peoples’ Friendship University of Russia in Moscow on August 22‒27, 2011. The category of papers on pseudo-differential operators contains such topics as elliptic operators assigned to diffeomorphisms of smooth manifolds, analysis on singular manifolds with edges, heat kernels and Green functions of sub-Laplacians on the Heisenberg group and Lie groups with more complexities than but closely related to the Heisenberg group, Lp-boundedness of pseudo-differential operators on the torus, and pseudo-differential operators related to time-frequency analysis. The second group of papers contains various classes of distributions and algebras of generalized functions with applications in linear and nonlinear differential equations, initial value problems and boundary value problems, stochastic and Malliavin-type differential equations. This second group of papers are related to the third collection of papers via the setting of Colombeau-type spaces and algebras in which microlocal analysis is developed by means of techniques in asymptotics. The volume contains the synergies of the three areas treated and is a useful complement to volumes 155, 164, 172, 189, 205 and 213 published in the same series in, respectively, 2004, 2006, 2007, 2009, 2010 and 2011.

Author : Anonim
Publisher : Allied Publishers
Page : 306 pages
File Size : 44,7 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 8177646001

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Analysis and Application by Anonim Pdf

Author : Ram Shankar Pathak
Publisher : Routledge
Page : 432 pages
File Size : 53,8 Mb
Release : 2017-07-05
Category : History
ISBN : 9781351562690

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Integral Transforms of Generalized Functions and Their Applications by Ram Shankar Pathak Pdf

For those who have a background in advanced calculus, elementary topology and functional analysis - from applied mathematicians and engineers to physicists - researchers and graduate students alike - this work provides a comprehensive analysis of the many important integral transforms and renders particular attention to all of the technical aspects of the subject. The author presents the last two decades of research and includes important results from other works.

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401512336

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author : Ahmed I. Zayed
Publisher : CRC Press
Page : 672 pages
File Size : 44,8 Mb
Release : 2019-08-21
Category : Mathematics
ISBN : 9780429610912

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Handbook of Function and Generalized Function Transformations by Ahmed I. Zayed Pdf

Function transformations, which include linear integral transformations, are some of the most important mathematical tools for solving problems in all areas of engineering and the physical sciences. They allow one to quickly solve a problem by breaking it down into a series of smaller, more manageable problems. The author has compiled the most important and widely used of these function transforms in applied mathematics and electrical engineering. In addition to classical transforms, newer transforms such as wavelets, Zak, and Radon are included. The book is neither a table of transforms nor a textbook, but it is a source book that provides quick and easy access to the most important properties and formulas of function and generalized function transformations. It is organized for convenient reference, with chapters broken down into the following sections: