Linear Operators: Spectral operators |
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Page 2029
RN 9 Similarly , functions on RN may determine tempered distributions just as they sometimes determine distributions . For example , since convergence on → in 0 is equivalent to the statement that for any two polynomials P , Q in N ...
RN 9 Similarly , functions on RN may determine tempered distributions just as they sometimes determine distributions . For example , since convergence on → in 0 is equivalent to the statement that for any two polynomials P , Q in N ...
Page 2184
... theorem that an arbitrary isomorphic homeomorphism of the algebra A ( B ) onto the algebra of continuous functions on its structure space may be represented by an integral with respect to a uniquely determined spectral measure .
... theorem that an arbitrary isomorphic homeomorphism of the algebra A ( B ) onto the algebra of continuous functions on its structure space may be represented by an integral with respect to a uniquely determined spectral measure .
Page 2316
Hence , in can only be a multiple pole of the resolvent of T if [ ( p < ( " ) ) ? dt = 0 . an t ) - = . Now , we have Pr ( t ) = sin snattan ) = sin ( snt + Bn ) , where Bn must be determined so as to satisfy kö lsn sin Bn = cos Bn . 1 ...
Hence , in can only be a multiple pole of the resolvent of T if [ ( p < ( " ) ) ? dt = 0 . an t ) - = . Now , we have Pr ( t ) = sin snattan ) = sin ( snt + Bn ) , where Bn must be determined so as to satisfy kö lsn sin Bn = cos Bn . 1 ...
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Contents
SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1931 |
Copyright | |
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adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension finite follows formal formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero
Bibliographic information
| Title | Linear Operators: Spectral operators Part 3 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure & Applied Mathematics : a Wiley-interscience series of texts, monographs & tracts Volume 7 of Pure and applied mathematics : a series of texts and monographs Volume 7 of Pure and applied mathematics Interscience Press Pure and applied mathematics, ISSN 0079-8185 Wiley classics library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | William G. Bade, Robert G. Bartle |
| Contributor | Karreman Mathematics Research Collection |
| Edition | reprint |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0471226394, 9780471226390 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |