Quasihomogeneous distributions
Grudzinski, Olaf von, 1947-
Quasihomogeneous distributions [electronic resource] / Olaf von Grudzinski. - 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. - 1 online resource (xviii, 449 p.) - North-Holland mathematics studies ; 165 . - North-Holland mathematics studies ; 165. .
Includes bibliographical references (p. 445-446) and index.
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.
9780444886705 0444886702
121809:124913 Elsevier Science & Technology http://www.sciencedirect.com
Theory of distributions (Functional analysis)
Distributions, Th�eorie des (Analyse fonctionnelle)
Distributions, th�eorie des (Analyse fonctionnelle)
Theory of distributions (Functional analysis)
Electronic books.
QA324 / .G78 1991eb
515/.782
Quasihomogeneous distributions [electronic resource] / Olaf von Grudzinski. - 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. - 1 online resource (xviii, 449 p.) - North-Holland mathematics studies ; 165 . - North-Holland mathematics studies ; 165. .
Includes bibliographical references (p. 445-446) and index.
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.
9780444886705 0444886702
121809:124913 Elsevier Science & Technology http://www.sciencedirect.com
Theory of distributions (Functional analysis)
Distributions, Th�eorie des (Analyse fonctionnelle)
Distributions, th�eorie des (Analyse fonctionnelle)
Theory of distributions (Functional analysis)
Electronic books.
QA324 / .G78 1991eb
515/.782
