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OverviewThis 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. Full Product DetailsAuthor: Robert M Kauffman (University of Alabama, Birming)Publisher: Taylor & Francis Ltd Imprint: CRC Press Volume: 355 Dimensions: Width: 21.00cm , Height: 1.00cm , Length: 28.00cm Weight: 0.276kg ISBN: 9780582276345ISBN 10: 0582276349 Pages: 152 Publication Date: 25 September 1996 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Unknown Availability: Out of stock Table of ContentsReviewsa concise monographic treatment like this has been lacking in the literature the general theory developed in this book will be of benefit for any analyst. -EMS Newsletter a concise monographic treatment like this has been lacking in the literature... the general theory developed in this book will be of benefit for any analyst. -EMS Newsletter Author InformationKauffman\, Robert M Tab Content 6Author Website:Countries AvailableAll regions |