Eigenfunction Expansions, Operator Algebras and Riemannian Symmetric Spaces (Chapman & Hall/CRC Research Notes in Mathematics Series) - Softcover

Kauffman, Robert M

Softcover

ISBN 10: 0582276349 ISBN 13: 9780582276345

Publisher: Chapman and Hall/CRC, 1996

Synopsis

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.

About this title

About the Author

Kauffman\, Robert M

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 1996
• Language: English
• ISBN 10: 0582276349
• ISBN 13: 9780582276345
• Binding: Paperback
• Edition number: 1
• Number of pages: 152