Elementary introduction to new generalized functions
Author(s)
Bibliographic Information
Elementary introduction to new generalized functions
（North-Holland mathematics studies, 113）（Notas de matemática, 103）
North-Holland , Sole distributor for the U.S.A. and Canada, Elsevier Science Pub. Co., 1985
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- : U.S.
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc19:515.7/c7162021270595
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Note
Bibliography: p. [278]-281
Includes index
Description and Table of Contents
Description
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.
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