C O R Generalized Functions Current Algebras And Control
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C O R Generalized Functions Current Algebras And Control
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Author : Robert Hermann
language : en
Publisher: Math Science Press
Release Date : 1994
C O R Generalized Functions Current Algebras And Control written by Robert Hermann and has been published by Math Science Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Nonlinear Theory Of Generalized Functions
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Author : Michael Oberguggenberger
language : en
Publisher: Routledge
Release Date : 2022-02-28
Nonlinear Theory Of Generalized Functions written by Michael Oberguggenberger and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-28 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.
On The Foundations Of Nonlinear Generalized Functions I And Ii
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Author : Michael Grosser
language : en
Publisher: American Mathematical Soc.
Release Date : 2001-07-03
On The Foundations Of Nonlinear Generalized Functions I And Ii written by Michael Grosser 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 2001-07-03 with Mathematics categories.
In part 1 we construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces, previous attempts in this direction are unified and completed. Several classification results are achieved and applications to nonlinear differential equations involving singularities are given. Part 2 gives a comprehensive analysis of algebras of Colombeau-type generalized functions in the range between the diffeomorphism-invariant quotient algebra ${\mathcal G}^d = {\mathcal E}_M/{\mathcal N}$ introduced in part 1 and Colombeau's original algebra ${\mathcal G}^e$. Three main results are established: First, a simple criterion describing membership in ${\mathcal N}$ (applicable to all types of Colombeau algebras) is given. Second, two counterexamples demonstrate that ${\mathcal G}^d$ is not injectively included in ${\mathcal G}^e$. Finally, it is shown that in the range ``between'' ${\mathcal G}^d$ and ${\mathcal G}^e$ only one more construction leads to a diffeomorphism invariant algebra. In analyzing the latter, several classification results essential for obtaining an intrinsic description of ${\mathcal G}^d$ on manifolds are derived.
Generalized Functions Operator Theory And Dynamical Systems
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Author : Ioannis Antoniou
language : en
Publisher: CRC Press
Release Date : 2021-02-25
Generalized Functions Operator Theory And Dynamical Systems written by Ioannis Antoniou and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-25 with Mathematics categories.
Nobel prize winner Ilya Prigogine writes in his preface: "Irreversibility is a challenge to mathematics...[which] leads to generalized functions and to an extension of spectral analysis beyond the conventional Hilbert space theory." Meeting this challenge required new mathematical formulations-obstacles met and largely overcome thanks primarily to the contributors to this volume." This compilation of works grew out of material presented at the "Hyperfunctions, Operator Theory and Dynamical Systems" symposium at the International Solvay Institutes for Physics and Chemistry in 1997. The result is a coherently organized collective work that moves from general, widely applicable mathematical methods to ever more specialized physical applications. Presented in two sections, part one describes Generalized Functions and Operator Theory, part two addresses Operator Theory and Dynamical Systems. The interplay between mathematics and physics is now more necessary than ever-and more difficult than ever, given the increasing complexity of theories and methods.
Generalized Functions
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Author :
language : en
Publisher:
Release Date : 1968
Generalized Functions written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with categories.
Nonlinear Theory Of Generalized Functions
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Author : Taylor & Francis Group
language : en
Publisher: CRC Press
Release Date : 2020-12-18
Nonlinear Theory Of Generalized Functions written by Taylor & Francis Group and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-18 with categories.
Covers the research relevant to work in partial differential equations, mathematical physics, and nonlinear analysis. With a focus on applications, this work provides a compilation of approaches to the problem of singularities in nonlinear models.
Nuclear Science Abstracts
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Author :
language : en
Publisher:
Release Date : 1974
Nuclear Science Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Nuclear energy categories.
Elementary Introduction To New Generalized Functions
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Author : Jean François Colombeau
language : en
Publisher: North Holland
Release Date : 1985
Elementary Introduction To New Generalized Functions 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 1985 with Distributions, Theory of (Functional analysis) 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, 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.
Generalized Functions
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Author :
language : en
Publisher:
Release Date : 1967
Generalized Functions written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
Generalized Functions For Applications
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Author : Bruce Desmond Craven
language : en
Publisher:
Release Date : 1984
Generalized Functions For Applications written by Bruce Desmond Craven and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Theory of distributions (Functional analysis) categories.