Linear Operators: Spectral theory |
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Page 898
If E is the resolution of the identity for the normal operator T and if d is a Borel set
of complex numbers , then E ( 8 ) T = TE ( 8 ) , 0 ( T8 ) CJ , where To is the
restriction of T to E ( ) . PROOF . The first statement follows from Theorem 1 ( ii ) .
If E is the resolution of the identity for the normal operator T and if d is a Borel set
of complex numbers , then E ( 8 ) T = TE ( 8 ) , 0 ( T8 ) CJ , where To is the
restriction of T to E ( ) . PROOF . The first statement follows from Theorem 1 ( ii ) .
Page 920
Under this assumption it will be shown that there is an ordered representation of
H onto = Lylēn , ) relative to T . It will follow from Theorem 10 that U and Ở are
equivalent . Let E and be the resolutions of the identity for T and † respectively .
Under this assumption it will be shown that there is an ordered representation of
H onto = Lylēn , ) relative to T . It will follow from Theorem 10 that U and Ở are
equivalent . Let E and be the resolutions of the identity for T and † respectively .
Page 1717
By induction on Jul , we can readily show that a formal identity ( 1 ) 2010 ( x ) 002
= C ( x ) 201 202 + £ C1 , 1 , 2 ; ( x ) , IJI < \ JI + J2L with suitable coefficients C ) , ,
, holds for every function C in CO ( 1 . ) . Making use of identities of the type ( 1 ) ...
By induction on Jul , we can readily show that a formal identity ( 1 ) 2010 ( x ) 002
= C ( x ) 201 202 + £ C1 , 1 , 2 ; ( x ) , IJI < \ JI + J2L with suitable coefficients C ) , ,
, holds for every function C in CO ( 1 . ) . Making use of identities of the type ( 1 ) ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
15 other sections not shown
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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero
Bibliographic information
| Title | Linear Operators: Spectral theory Part 2 of Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics : a series of texts and monographs Volume 7 of Pure and applied mathematics Interscience Press Volume 7 of Pure and applied mathematics Wiley Classics Library |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Contributor | Karreman Mathematics Research Collection |
| Publisher | Interscience Publishers, 1958 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0470226382, 9780470226384 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |