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Linear Theory of Colombeau Generalized Functions

1998-05-20 Mathematics
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Release : 1998-05-20
Genre : Mathematics
Kind : eBook
Book Rating : 832/5 ( reviews)

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Book Synopsis Linear Theory of Colombeau Generalized Functions by : M Nedeljkov

Download or read book Linear Theory of Colombeau Generalized Functions written by M Nedeljkov. This book was released on 1998-05-20. Available in PDF, EPUB and Kindle. Book excerpt: 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.

New Generalized Functions and Multiplication of Distributions

2000-04-01 Science
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Release : 2000-04-01
Genre : Science
Kind : eBook
Book Rating : 95X/5 ( reviews)

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Book Synopsis New Generalized Functions and Multiplication of Distributions by : J.F. Colombeau

Download or read book New Generalized Functions and Multiplication of Distributions written by J.F. Colombeau. This book was released on 2000-04-01. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Elementary Introduction to New Generalized Functions

2011-08-18 Mathematics
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Release : 2011-08-18
Genre : Mathematics
Kind : eBook
Book Rating : 247/5 ( reviews)

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Book Synopsis Elementary Introduction to New Generalized Functions by : J.F. Colombeau

Download or read book Elementary Introduction to New Generalized Functions written by J.F. Colombeau. This book was released on 2011-08-18. Available in PDF, EPUB and Kindle. Book excerpt: 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

2006-11-15 Mathematics
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Release : 2006-11-15
Genre : Mathematics
Kind : eBook
Book Rating : 109/5 ( reviews)

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Book Synopsis Multiplication of Distributions by : Jean F. Colombeau

Download or read book Multiplication of Distributions written by Jean F. Colombeau. This book was released on 2006-11-15. Available in PDF, EPUB and Kindle. Book excerpt: 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).

C-O-R Generalized Functions, Current Algebras, and Control

1994 Mathematics
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Release : 1994
Genre : Mathematics
Kind : eBook
Book Rating : 460/5 ( reviews)

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Book Synopsis C-O-R Generalized Functions, Current Algebras, and Control by : Robert Hermann

Download or read book C-O-R Generalized Functions, Current Algebras, and Control written by Robert Hermann. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt:

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