UID:
almahu_9949698076802882
Format:
1 online resource (297 p.)
ISBN:
1-281-78834-1
,
9786611788346
,
0-08-087224-7
Series Statement:
North-Holland mathematics studies ; 113
Content:
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 C8 functions of several real variables and with some rudiments of integration theory. Part II defines tempered generali
Note:
Description based upon print version of record.
,
Front Cover; Elementry Introduction to New Generalized Functions; Copyright Page; Contents; PART I: AN ELEMENTARY APPROACH TO THE NEW GENERALIZED FUNCTIONS; Chapter 1. Generalized Functions; 1.1 - Definition of the generalized functions on IRn; 1.2 -- Generalized functions on an open set O ? IRn; 1.3 - Local properties of generalized functions; 1.4 - Nonlinear properties of generalized functions; 1.5 - Distributions: definitions and examples; Chapter 2. Generalized Analysis; 2.1 - Generalized numbers and pointvalues of generalized functions
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2.2 - The integration on compact sets of generalized functions2.3 - Primitives; 2.4 - Application to distributions; 2.5 - Generalized distributions; Chapter 3. Some Linear Cauchy Problems; 3.1 - Introduction; 3.2 - Existence and Uniqueness Results; 3.3 - Approximate and Asymptotic expansions of generalized functions; 3.4 - The equation X' = ig AX in the non communicative case; 3.5 - The equation X' = ig AX when A has no compact support; PART II: TEMPERED GENERALIZED FUNCTIONS; Chapter 4. The Fourier Transform and the Tempered Generalized Functions; 4.1 - The tempered generalized functions
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4.2 - Integration of the tempered generalized functions4.3 - The Fourier transform of the tempered generalized functions; 4.4 - The tempered distributions; Chapter 5. The Convolution Product; 5.1 - Convolution of generalized functions; 5.2 - Convolution of distributions; 5.3 - Convolution of tempered generalized functions; Chapter 6. Computations on Tempered Generalized Functions; 6.1 - Introduction; 6.2 - The vector valued tempered generalized functions; 6.3 - The free field; 6.4 - Computations; PAR T III: NEW SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS; Chapter 7. Linear Equations
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7.1 -- The ? equation7.2 - A Cauchy problem for linear wave equations; 7.3 - A linear Cauchy-Kovalevska theorem; Chapter 8. Nonlinear Equations; 8.1 - An existence result for wave equations including a nonlinear term with a boundedness property; 8.2 - Uniqueness and regularity results; 8.3 - An existence result for wave equations with unbounded second members; 8.4 - A regularity result; Appendix 1 The Removal of Divergences in Perturbation Theory; Appendix 2 Generalized Functions on Closed Sets and Whitney 's Extension Theorem
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Appendix 3 Generalized Functions and Waelbroeck 's Analysis in Quotient SpacesAppendix 4 Generalized Functions on Hilbert Spaces; Appendix 5 Complements to N G.F. : Analytic Continuation and Composition of Generalized Functions; Appendix 6 General Existence Results for Linear Partial Differential Equations with C8 Coefficients; Appendix 7 Introduction to Distributions and their Multiplication for First Year University Students; Bibliographic Notes; Index; References
,
English
Additional Edition:
ISBN 0-444-87756-8
Language:
English
