New Generalized Functions And Multiplication Of Distributions

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New Generalized Functions And Multiplication Of Distributions

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Author : Jean François Colombeau
language : en
Publisher: North Holland
Release Date : 1984-01-01

New Generalized Functions And Multiplication Of Distributions written by Jean François Colombeau and has been published by North Holland this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-01-01 with Distributions, Theory of (Functional analysis) categories.

This volume presents a new mathematical theory of generalized functions, more general than Distribution Theory, giving a rigorous mathematical sense to any product of a finite number of distributions and to heuristic computations of Quantum Field Theory. Although the physical motivations are emphasized, the book is also addressed to mathematicians with no knowledge of physics. This work opens a new domain of research in both pure and applied mathematics.

New Generalized Functions And Multiplication Of Distributions

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Author : J.F. Colombeau
language : en
Publisher: Elsevier
Release Date : 2000-04-01

New Generalized Functions And Multiplication Of Distributions written by J.F. Colombeau and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Science categories.

This volume presents a new mathematical theory of generalized functions, more general than Distribution Theory, giving a rigorous mathematical sense to any product of a finite number of distributions and to heuristic computations of Quantum Field Theory. Although the physical motivations are emphasized, the book is also addressed to mathematicians with no knowledge of physics. This work opens a new domain of research in both pure and applied mathematics.

New Generalized Functions And Multiplication Of Distributions

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Author : Jean François Colombeau
language : en
Publisher:
Release Date : 1984

New Generalized Functions And Multiplication Of Distributions written by Jean François Colombeau and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.

Elementary Introduction To New Generalized Functions

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Author : J.F. Colombeau
language : en
Publisher: Elsevier
Release Date : 2011-08-18

Elementary Introduction To New Generalized Functions written by J.F. Colombeau and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.

The author's previous book `New Generalized Functions and Multiplication of Distributions' (North-Holland, 1984) introduced `new generalized functions' in order to explain heuristic computations of Physics and to give a meaning to any finite product of distributions. The aim here is to present these functions in a more direct and elementary way. In Part I, the reader is assumed to be familiar only with the concepts of open and compact subsets of R&eegr;, of C∞ functions of several real variables and with some rudiments of integration theory. Part II defines tempered generalized functions, i.e. generalized functions which are, in some sense, increasing at infinity no faster than a polynomial (as well as all their partial derivatives). Part III shows that, in this setting, the partial differential equations have new solutions. The results obtained show that this setting is perfectly adapted to the study of nonlinear partial differential equations, and indicate some new perspectives in this field.

Multiplication Of Distributions

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Author : Jean F. Colombeau
language : en
Publisher: Springer
Release Date : 2006-11-15

Multiplication Of Distributions written by Jean F. Colombeau and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

This book presents recent and very elementary developments of a theory of multiplication of distributions in the field of explicit and numerical solutions of systems of PDEs of physics (nonlinear elasticity, elastoplasticity, hydrodynamics, multifluid flows, acoustics). The prerequisites are kept to introductory calculus level so that the book remains accessible at the same time to pure mathematicians (as a smoothand somewhat heuristic introdcution to this theory) and to applied mathematicians, numerical engineers and theoretical physicists (as a tool to treat problems involving products of distributions).

Nonlinear Theory Of Generalized Functions

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Author : Michael Oberguggenberger
language : en
Publisher: CRC Press
Release Date : 1999-03-16

Nonlinear Theory Of Generalized Functions written by Michael Oberguggenberger and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-03-16 with Mathematics categories.

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.

Qualitative Properties Of Dispersive Pdes

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Author : Vladimir Georgiev
language : en
Publisher: Springer Nature
Release Date : 2022-12-02

Qualitative Properties Of Dispersive Pdes written by Vladimir Georgiev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-02 with Mathematics categories.

This book provides a valuable collection of contributions by distinguished scholars presenting the state of the art and some of the most significant latest developments and future challenges in the field of dispersive partial differential equations. The material covers four major lines: (1) Long time behaviour of NLS-type equations, (2) probabilistic and nonstandard methods in the study of NLS equation, (3) dispersive properties for heat-, Schrödinger-, and Dirac-type flows, (4) wave and KdV-type equations. Across a variety of applications an amount of crucial mathematical tools are discussed, whose applicability and versatility goes beyond the specific models presented here. Furthermore, all contributions include updated and comparative literature.

Stochastic Processes Physics And Geometry Ii Proceedings Of The Iii International Conference

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Author : Sergio Albeverio
language : en
Publisher: World Scientific
Release Date : 1995-02-17

Stochastic Processes Physics And Geometry Ii Proceedings Of The Iii International Conference written by Sergio Albeverio and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-02-17 with categories.

As was already evident from the previous two meetings, the theory of stochastic processes, the study of geometrical structures, and the investigation of certain physical problems are inter-related. In fact the trend in recent years has been towards stronger interactions between these areas. As a result, a large component of the contributions is concerned with the theory of stochastic processes, quantum theory, and their relations.

Solution Of Continuous Nonlinear Pdes Through Order Completion

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Author : M.B. Oberguggenberger
language : en
Publisher: Elsevier
Release Date : 1994-07-14

Solution Of Continuous Nonlinear Pdes Through Order Completion written by M.B. Oberguggenberger and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-07-14 with Mathematics categories.

This work inaugurates a new and general solution method for arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need not satisfy any kind of monotonicity properties. Moreover, the solution method is completely type independent. In other words, it does not assume anything about the nonlinear PDEs, except for the continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any discontinuous and measurable function.

Developments In Nonstandard Mathematics

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Author : Nigel J Cutland
language : en
Publisher: CRC Press
Release Date : 2020-01-30

Developments In Nonstandard Mathematics written by Nigel J Cutland and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-30 with Mathematics categories.

This book contains expository papers and articles reporting on recent research by leading world experts in nonstandard mathematics, arising from the International Colloquium on Nonstandard Mathematics held at the University of Aveiro, Portugal in July 1994. Nonstandard mathematics originated with Abraham Robinson, and the body of ideas that have developed from this theory of nonstandard analysis now vastly extends Robinson's work with infinitesimals. The range of applications includes measure and probability theory, stochastic analysis, differential equations, generalised functions, mathematical physics and differential geometry, moreover, the theory has implicaitons for the teaching of calculus and analysis. This volume contains papers touching on all of the abovbe topics, as well as a biographical note about Abraham Robinson based on the opening address given by W.A>J> Luxemburg - who knew Robinson - to the Aveiro conference which marked the 20th anniversary of Robinson's death. This book will be of particular interest to students and researchers in nonstandard analysis, measure theory, generalised functions and mathematical physics.