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Quasihomogeneous distributions

Author: Olaf von Grudzinski
Publisher: Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A : Distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1991.
Series: North-Holland mathematics studies, 165.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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 the central tool for the study of the solvability of quasihomogeneous multiplication equations and of quasihomogeneous partial differential equations with constant coefficients.  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Grudzinski, Olaf von, 1947-
Quasihomogeneous distributions.
Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A : Distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1991
(DLC) 90023029
(OCoLC)22733022
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Olaf von Grudzinski
ISBN: 9780444886705 0444886702 9780080872766 008087276X
OCLC Number: 316570241
Description: 1 online resource (xviii, 449 pages).
Contents: Front Cover; Quasihomogeneous Distributions; Copyright Page; Contents; Introduction; Notation; List of Symbols; Chapter I. (Almost) Quasihomogeneous Functions. Definitions and Basic Properties; Chapter II. (Almost) Quasihomogeneous Distributions. Definitions and Basic Properties; Chapter III. Constructing (Almost) Quasihomogeneous Functions by Taking Quasihomogeneous Averages of Functions with M-bounded Support; Chapter IV. Constructing (Almost) Quasihomogeneous Distributions by Taking Quasihomogeneous Averages . The Case: X is Locally M-bounded.
Series Title: North-Holland mathematics studies, 165.
Responsibility: Olaf von Grudzinski.

Abstract:

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 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 Schr̲dinger 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 Schr̲dinger equation.

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