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Quasihomogeneous Distributions O. Von Grudzinski

Quasihomogeneous Distributions

O. Von Grudzinski

Published January 24th 1991
ISBN : 9780080872766
ebook
469 pages
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 About the Book 

This is a systematic exposition of the basics of the theory of quasihomogeneous (in particular, homogeneous) functions and distributions (generalized functions). A major theme is the method of taking quasihomogeneous averages. It serves as theMoreThis is a systematic exposition of the basics of the theory of quasihomogeneous (in particular, homogeneous) functions and distributions (generalized functions). A major theme is the method of taking quasihomogeneous averages. It serves as the central tool for the study of the solvability of quasihomogeneous multiplication equations and of quasihomogeneous partial differential equations with constant coefficients. Necessary and sufficient conditions for solvability are given. Several examples are treated in detail, among them the heat and the SchrAdinger equation. The final chapter is devoted to quasihomogeneous wave front sets and their application to the description of singularities of quasihomogeneous distributions, in particular to quasihomogeneous fundamental solutions of the heat and of the SchrAdinger equation.