Quasihomogeneous distributions [electronic resource] / Olaf von Grudzinski.
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TextSeries: North-Holland mathematics studies ; 165.Publication details: Amsterdam ; New York : New York, N.Y., U.S.A : North-Holland ; Distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1991. Description: 1 online resource (xviii, 449 p.)ISBN: 9780444886705; 0444886702Subject(s): Theory of distributions (Functional analysis) | Distributions, Th�eorie des (Analyse fonctionnelle) | Distributions, th�eorie des (Analyse fonctionnelle) | Theory of distributions (Functional analysis)Genre/Form: Electronic books.Additional physical formats: Print version:: Quasihomogeneous distributions.DDC classification: 515/.782 LOC classification: QA324 | .G78 1991ebOnline resources: ScienceDirect | Volltext 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. Necessary and sufficient conditions for solvability are given. Several examples are treated in detail, among them the heat and the Sch�rdinger 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 Sch�rdinger equation.
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 Sch�rdinger 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 Sch�rdinger equation.
Includes bibliographical references (p. 445-446) and index.
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