Linear Operators: Spectral theory |
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Page 898
If we put E ( d ) = 0 ) when d n ( T ) is void , then Corollary 4 follows immediately
from Theorem 1 and Corollary IX . 3 . 15 . Q . E . D . 5 DEFINITION . The uniquely
defined spectral measure associated , in Corollary 4 , with the normal operator T
...
If we put E ( d ) = 0 ) when d n ( T ) is void , then Corollary 4 follows immediately
from Theorem 1 and Corollary IX . 3 . 15 . Q . E . D . 5 DEFINITION . The uniquely
defined spectral measure associated , in Corollary 4 , with the normal operator T
...
Page 1142
14 . Q . E . D . In what follows , we will use the symbols p and n to denote the
continuous extension to the classes C , of operators of the mappings p and n of
the previous lemma . We will also write t = ( tn ) / 2 . We note the following
corollary .
14 . Q . E . D . In what follows , we will use the symbols p and n to denote the
continuous extension to the classes C , of operators of the mappings p and n of
the previous lemma . We will also write t = ( tn ) / 2 . We note the following
corollary .
Page 1301
Proceeding inductively we see that v6k ) ( b ) = 0 , 0 Sk 5 2n - 1 . However , as vo
satisfies an equation of order 2n , v , must be identically zero . This contradiction
completes the proof . Q . E . D . 23 COROLLARY . Let T be a formal differential ...
Proceeding inductively we see that v6k ) ( b ) = 0 , 0 Sk 5 2n - 1 . However , as vo
satisfies an equation of order 2n , v , must be identically zero . This contradiction
completes the proof . Q . E . D . 23 COROLLARY . Let T be a formal differential ...
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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 |