Linear Operators: Spectral theory |
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Page 995
Let h be in L ( R ) with himo ) = 1 and h vanishing on an open set containing the
remainder of olf * ° ) . It follows from Lemma 12 that the set ( h * f * 9 ) contains at
most the single point m , and hence , from Theorem 16 and Lemma 3 . 1 ( d ) ,
that ...
Let h be in L ( R ) with himo ) = 1 and h vanishing on an open set containing the
remainder of olf * ° ) . It follows from Lemma 12 that the set ( h * f * 9 ) contains at
most the single point m , and hence , from Theorem 16 and Lemma 3 . 1 ( d ) ,
that ...
Page 996
Thus , by hypothesis , olf * 9 ) contains an isolated point which contradicts
Lemma 19 . Q . E . D . The next result shows in a striking manner the relations
between the study of spectral synthesis and the original L , closure theorem of N .
Wiener .
Thus , by hypothesis , olf * 9 ) contains an isolated point which contradicts
Lemma 19 . Q . E . D . The next result shows in a striking manner the relations
between the study of spectral synthesis and the original L , closure theorem of N .
Wiener .
Page 1397
The method of proof is the following : it will be shown that if the theorem is false ,
then a proper symmetric extension T , of T can be constructed whose domain
properly contains both D ( T ) and the null - space of T * . This readily yields a ...
The method of proof is the following : it will be shown that if the theorem is false ,
then a proper symmetric extension T , of T can be constructed whose domain
properly contains both D ( T ) and the null - space of T * . This readily yields a ...
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 869 |
Commutative BAlgebras | 877 |
Copyright | |
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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero
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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, 1963 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| ISBN | 0470226382, 9780470226384 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |