Generalized Functions Convergence Structures And Their Applications

Author : Bogoljub Stankovic
Publisher : Springer Science & Business Media
Page : 432 pages
File Size : 50,5 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 : Bogoljub Stankovic
Publisher : Unknown
Page : 468 pages
File Size : 55,8 Mb
Release : 1988-09-01
Category : Electronic
ISBN : 1461310563

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

Author : Anonim
Publisher : Unknown
Page : 68 pages
File Size : 55,8 Mb
Release : 1987
Category : Electronic
ISBN : OCLC:438882069

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Generalized functions, convergence structures and their applications by Anonim Pdf

Author : Piotr Antosik,Andrzej Kaminski
Publisher : World Scientific
Page : 398 pages
File Size : 43,5 Mb
Release : 1990-09-12
Category : Electronic
ISBN : 9789814611718

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Generalized Functions And Convergence: Memorial Volume For Professor Jan Mikusinski by Piotr Antosik,Andrzej Kaminski Pdf

The conference was devoted to the memory of the late Professor Jan Mikusinski. The proceedings is divided into three parts. The first one contains biographical materials and memoirs about Professor Mikusinski and his work. The second part is devoted to the theory of generalized functions and the third to convergence structures.

Author : Ram Shankar Pathak
Publisher : Routledge
Page : 432 pages
File Size : 40,5 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 : M Nedeljkov,S Pilipovic,D Scarpalezos
Publisher : CRC Press
Page : 172 pages
File Size : 53,9 Mb
Release : 1998-05-20
Category : Mathematics
ISBN : 0582356830

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Linear Theory of Colombeau Generalized Functions by M Nedeljkov,S Pilipovic,D Scarpalezos Pdf

Results from the now-classical distribution theory involving convolution and Fourier transformation are extended to cater for Colombeau's generalized functions. Indications are given how these particular generalized functions can be used to investigate linear equations and pseudo differential operators. Furthermore, applications are also given to problems with nonregular data.

Author : Ahmed I. Zayed
Publisher : CRC Press
Page : 672 pages
File Size : 55,9 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:

Author : R.S. Pathak
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 51,5 Mb
Release : 2013-11-11
Category : Social Science
ISBN : 9781489915917

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Generalized Functions and Their Applications by R.S. Pathak Pdf

The International Symposium on Generalized Functions and Their Applications was organized by the Department of Mathematics, Banaras Hindu University, and held December 23-26, 1991, on the occasion of the Platinum Jubilee Celebration of the university. More than a hundred mathematicians from ten countries participated in the deliberations of the symposium. Thirty lectures were delivered on a variety of topics within the area. The contributions to the proceedings of the symposium are, with a few exceptions, expanded versions of the lectures delivered by the invited speakers. The survey papers by Komatsu and Hoskins and Sousa Pinto provide an up-to-date account of the theory of hyperfunctions, ultradistributions and microfunctions, and the nonstandard theory of new generalized functions, respectively; those by Stankovic and Kanwal deal with structures and asymptotics. Choquet-Bruhat's work studies generalized functions on manifold and gives applications to shocks and discrete models. The other contributions relate to contemporary problems and achievements in theory and applications, especially in the theory of partial differential equations, differential geometry, mechanics, mathematical physics, and systems science. The proceedings give a very clear impression of the present state of the art in this field and contain many challenges, ideas, and open problems. The volume is very helpful for a broad spectrum of readers: graduate students to mathematical researchers.

Author : M. Husek,J. van Mill
Publisher : Elsevier
Page : 808 pages
File Size : 49,8 Mb
Release : 1992-11-20
Category : Mathematics
ISBN : 9780080934433

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Recent Progress in General Topology by M. Husek,J. van Mill Pdf

These papers survey the developments in General Topology and the applications of it which have taken place since the mid 1980s. The book may be regarded as an update of some of the papers in the Handbook of Set-Theoretic Topology (eds. Kunen/Vaughan, North-Holland, 1984), which gives an almost complete picture of the state of the art of Set Theoretic Topology before 1984. In the present volume several important developments are surveyed that surfaced in the period 1984-1991. This volume may also be regarded as a partial update of Open Problems in Topology (eds. van Mill/Reed, North-Holland, 1990). Solutions to some of the original 1100 open problems are discussed and new problems are posed.

Author : Ram P. Kanwal
Publisher : Springer Science & Business Media
Page : 502 pages
File Size : 54,9 Mb
Release : 2004-07-23
Category : Mathematics
ISBN : 0817643435

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Generalized Functions by Ram P. Kanwal Pdf

Provides a more cohesive and sharply focused treatment of fundamental concepts and theoretical background material, with particular attention given to better delineating connections to varying applications Exposition driven by additional examples and exercises

Author : R. Beattie,Heinz-Peter Butzmann
Publisher : Springer Science & Business Media
Page : 272 pages
File Size : 43,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401599429

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Convergence Structures and Applications to Functional Analysis by R. Beattie,Heinz-Peter Butzmann Pdf

This text offers a rigorous introduction into the theory and methods of convergence spaces and gives concrete applications to the problems of functional analysis. While there are a few books dealing with convergence spaces and a great many on functional analysis, there are none with this particular focus. The book demonstrates the applicability of convergence structures to functional analysis. Highlighted here is the role of continuous convergence, a convergence structure particularly appropriate to function spaces. It is shown to provide an excellent dual structure for both topological groups and topological vector spaces. Readers will find the text rich in examples. Of interest, as well, are the many filter and ultrafilter proofs which often provide a fresh perspective on a well-known result. Audience: This text will be of interest to researchers in functional analysis, analysis and topology as well as anyone already working with convergence spaces. It is appropriate for senior undergraduate or graduate level students with some background in analysis and topology.

Author : I. M. Gel′fand,G. E. Shilov
Publisher : American Mathematical Soc.
Page : 423 pages
File Size : 53,9 Mb
Release : 2016-04-19
Category : Theory of distributions (Functional analysis)
ISBN : 9781470426583

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Generalized Functions, Volume 1 by I. M. Gel′fand,G. E. Shilov Pdf

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 : Michael Oberguggenberger,Michael Grosser,Michael Kunzinger,Gunther Hormann
Publisher : Routledge
Page : 400 pages
File Size : 46,6 Mb
Release : 2022-02-28
Category : Mathematics
ISBN : 9781351428033

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Nonlinear Theory of Generalized Functions by Michael Oberguggenberger,Michael Grosser,Michael Kunzinger,Gunther Hormann Pdf

Questions regarding the interplay of nonlinearity and the creation and propagation of singularities arise in a variety of fields-including nonlinear partial differential equations, noise-driven stochastic partial differential equations, general relativity, and geometry with singularities. A workshop held at the Erwin-Schrödinger International Institute for Mathematical Physics in Vienna investigated these questions and culminated in this volume of invited papers from experts in the fields of nonlinear partial differential equations, structure theory of generalized functions, geometry and general relativity, stochastic partial differential equations, and nonstandard analysis. The authors provide the latest research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this books provides a compilation of recent approaches to the problem of singularities in nonlinear models. The theory of differential algebras of generalized functions serves as the central theme of the project, along with its interrelations with classical methods.

Author : Sergio Albeverio,Wilhelm A.J. Luxemburg,Manfred P.H. Wolff
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 51,9 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9789401584517

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Advances in Analysis, Probability and Mathematical Physics by Sergio Albeverio,Wilhelm A.J. Luxemburg,Manfred P.H. Wolff Pdf

In 1961 Robinson introduced an entirely new version of the theory of infinitesimals, which he called `Nonstandard analysis'. `Nonstandard' here refers to the nature of new fields of numbers as defined by nonstandard models of the first-order theory of the reals. This system of numbers was closely related to the ring of Schmieden and Laugwitz, developed independently a few years earlier. During the last thirty years the use of nonstandard models in mathematics has taken its rightful place among the various methods employed by mathematicians. The contributions in this volume have been selected to present a panoramic view of the various directions in which nonstandard analysis is advancing, thus serving as a source of inspiration for future research. Papers have been grouped in sections dealing with analysis, topology and topological groups; probability theory; and mathematical physics. This volume can be used as a complementary text to courses in nonstandard analysis, and will be of interest to graduate students and researchers in both pure and applied mathematics and physics.

Author : Stevan Pilipovic,Bogoljub Stankovic,Jasson Vindas
Publisher : World Scientific
Page : 309 pages
File Size : 50,7 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.