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 olt * ) . It follows from Lemma 12 that the set ( h * f * ° ) contains at most the single point m , and hence , from Theorem 16 and Lemma ...
Let h be in L ( R ) with himo ) ( = 1 and h : vanishing on an open set containing the remainder of olt * ) . It follows from Lemma 12 that the set ( h * f * ° ) contains at most the single point m , and hence , from Theorem 16 and Lemma ...
Page 996
From Lemma 12 ( b ) it is seen that olf * ) Cole ) and from Lemma 12 ( c ) and the equation if = tf it follows that olf * q ) contains no interior point of o ( q ) . Hence of * v ) is a closed subset of the boundary of o ( q ) .
From Lemma 12 ( b ) it is seen that olf * ) Cole ) and from Lemma 12 ( c ) and the equation if = tf it follows that olf * q ) contains no interior point of o ( q ) . Hence of * v ) is a closed subset of the boundary of o ( q ) .
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 * .
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 * .
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Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
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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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique 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 |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1963 |
| Original from | the University of Michigan |
| Digitized | 20 Nov 2007 |
| ISBN | 0471226386, 9780471226383 |
| Length | 2592 pages |
| Export Citation | BiBTeX EndNote RefMan |