Eigenfunction Expansions, Operator Algebras and Riemannian Symmetric Spaces (Pitman Research Notes in Mathematics Series, 355) - Robert M Kauffman, Robert M. Kauffman (1996)
ISBN 0582276349
Subject Eigenfunction expansions; Operator theory
Publisher Chapman & Hall/CRC
Publication Date 9/25/1996
Format Hardcover (249 x 163 mm)
Language e

This Research Note pays particular attention to studying the convergence of the expansion and to the case where D is a family of partial differential operators. All operators in the natural von Neumann algebraassociated with D, and also unbounded operators affiliated with this algebra, are expanded simultaneously in terms of generalized eigenprojections. These are operators which carry a natural space associated with D into its dual. The elements of the range of these eigenprojections are the eigenfunctions, which solve the appropriate eigenvalue equations by duality. The spectral measure is abstractly defined, but its absolute continuity with respect to Hausdorf measure on the joint spectrum is shown to occur when the eigenfunctions are very well-behaved. Uniqueness results are given showing that any two expansions arise from each other by a simple change of variable. A considerable effort has been made to keep the book self-contained for readers with a background in functional analysis including a basic understanding of the theory of von Neumann algebras. More advanced topics in functional analysis, andan introduction to differential geometry and differential operator theory, mostly without proofs, are given in an extensive section on background material.

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Product Details
LoC Classification QA329. K38 1996 copy
Dewey 515/.7242
Cover Price $119.95
No. of Pages 152