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Elementary Introduction to New Generalized Functions - 1st Edition - ISBN: 9780444877567, 9780080872247

Elementary Introduction to New Generalized Functions, Volume 113

1st Edition

Author: J.F. Colombeau
eBook ISBN: 9780080872247
Imprint: North Holland
Published Date: 1st April 2000
Page Count: 280
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The author's previous book New Generalized Functions and Multiplication of Distributions' (North-Holland, 1984) introducednew 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.


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© North Holland 1985
1st April 2000
North Holland
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J.F. Colombeau