Elementary Introduction to New Generalized Functions - Softcover

Colombeau, Jean Francois

Softcover

ISBN 10: 0444558098 ISBN 13: 9780444558091

Publisher: North Holland, 2012

Synopsis

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.

Edition details

• Publisher: North Holland
• Publication date: 2012
• Language: English
• ISBN 10: 0444558098
• ISBN 13: 9780444558091
• Binding: Paperback
• Number of pages: 296