Linear Operators: Spectral theory |
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Page 1064
... subsequence , we may assume that gm ( x ) = Q ( x ) for almost all x . But it is
clear that gm ( x ) = g ( x ) for all x . Hence q = g , proving that ( gl , 51 , 111 , if f is
in Co ( I ) and vanishes outside a bounded set . Next let | be in L ( E ” ) , and let {
Im } ...
... subsequence , we may assume that gm ( x ) = Q ( x ) for almost all x . But it is
clear that gm ( x ) = g ( x ) for all x . Hence q = g , proving that ( gl , 51 , 111 , if f is
in Co ( I ) and vanishes outside a bounded set . Next let | be in L ( E ” ) , and let {
Im } ...
Page 1120
Throughout the present section , we assume for simplicity of statement that
Hilbert space is separable . Subdiagonal representations of an operator are
connected with the study of its invariant subspaces . Thus , the key to the situation
that we ...
Throughout the present section , we assume for simplicity of statement that
Hilbert space is separable . Subdiagonal representations of an operator are
connected with the study of its invariant subspaces . Thus , the key to the situation
that we ...
Page 1734
Since we have only to show that ff is in H ( k + 1 ) ( UI ) for some neighborhood U
CU , of p , it is clear that we may assume without loss of generality that U2 = U ,
70 = 1 . This will be assumed in what follows . Making use of the properties ( i ) ...
Since we have only to show that ff is in H ( k + 1 ) ( UI ) for some neighborhood U
CU , of p , it is clear that we may assume without loss of generality that U2 = U ,
70 = 1 . This will be assumed in what follows . Making use of the properties ( i ) ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
15 other sections not shown
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Common terms and phrases
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 |