UID:
almahu_9947368002502882
Format:
1 online resource (469 p.)
ISBN:
1-281-78925-9
,
9786611789251
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0-08-087276-X
Series Statement:
North-Holland mathematics studies ; 165
Content:
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 Schrödinger equation. The final chapter is devoted
Note:
Description based upon print version of record.
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Chapter II. (Almost) Quasihomogeneous Distributions. Definitions and Basic Properties(a) Quasihomogeneous Distributions; (b) The Fourier Transform of Quasihomogeneous Distributions; (c) Meromorphic Functions of Quasihomogeneous Distribution; (d) Almost Quasihomogeneous Distributions; (e) Meromorphic Functions of Almost Quasihomogeneous Distributions; (f) Appendix: (G,σ7) -invariant Distributions; Chapter III. Constructing (Almost) Quasihomogeneous Functions by Taking Quasihomogeneous Averages of Functions with M-bounded Support; (a) Introducing the Quasihomogeneous Averages f m.w
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(b) (M,I)-bounded Subsets of X(c) When is Every Compact Subset of X M-bounded?; (d) Describing Quasihomogeneous Functions on X as Quasihomogeneous Averages; Chapter IV. Constructing (Almost) Quasihomogeneous Distributions by Taking Quasihomogeneous Averages . The Case: X is Locally M-bounded; (a) Introducing the Quasihomogeneous Averages um,w; (b) Describing Quasihomogeneous Distributions in Terms of Quasihomogeneous Averages; (c) Solving the Equation (dM - m) S = T; (d) Singular Support and Wave Front Sets of the Distributions u,mw
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Chapter VI. Constructing (Almost) Quasihomogeneous Distributions by Taking Quasihomogeneous Averages . The Case: (1.14) holds(a) Weakly (M.I).bounded Subsets of X; (b) The Distributions urn,w and Their Basic Properties; (c) Describing the Almost Quasihomogeneous Distributions on X with Support Contained in X \ X +; (d) Characterizing (Almost) Quasihomogeneous Distributions on X in Terms of Quasihomogeneous Averages; (e) Solving the Equation ( dm - m ) S = T; (f ) Duality Brackets for the Spaces Qrn(mq) and um.k (mq) ,
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Chapter VII . Solvability of Quasihomogeneous Multiplication Equations and Partial Differential Equations
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English
Additional Edition:
ISBN 0-444-88670-2
Language:
English
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