Eigenfunction Expansions, Operator Algebras and Riemannian Symmetric Spaces

1. Auflage 1996
ISBN: 978-0-582-27634-5
Verlag: Chapman and Hall/CRC

Buch, Englisch, Band 355, 152 Seiten, Format (B × H): 163 mm x 249 mm, Gewicht: 272 g

Reihe: Chapman & Hall/CRC Research Notes in Mathematics Series

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.

Autoren/Hrsg.

Kauffman, Robert M.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

1 Introduction2 Some background material3 Generalized eigenprojection expansions4 Eigenfunction expansions on Cn5 When A exists6 Differential operators on Riemannian manifolds7 Operator algebras and symmetric spaces8 Spaces of noncompact type

Über Autor(innen)

Kauffman\, Robert M