Linear Operators, Part 2 |
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Page 1239
Conversely , let T , be a self adjoint extension of T. Then by Lemma 26 , T , is the restriction of T * to a subspace W of D ( T * ) determined by a symmetric family of linearly independent boundary conditions Bi ( x ) = 0 , i 1 , ...
Conversely , let T , be a self adjoint extension of T. Then by Lemma 26 , T , is the restriction of T * to a subspace W of D ( T * ) determined by a symmetric family of linearly independent boundary conditions Bi ( x ) = 0 , i 1 , ...
Page 1270
Extensions of symmetric operators . The problem of determining whether a given symmetric operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed .
Extensions of symmetric operators . The problem of determining whether a given symmetric operator has a self adjoint extension is of crucial importance in determining whether the spectral theorem may be employed .
Page 1397
Q.E.D. It follows from Theorem 5 and Corollary 4 that the set of nonisolated points of the spectrum of a self adjoint extension T of T. ( t ) is independent of the particular extension chosen , i.e. , is independent of the particular ...
Q.E.D. It follows from Theorem 5 and Corollary 4 that the set of nonisolated points of the spectrum of a self adjoint extension T of T. ( t ) is independent of the particular extension chosen , i.e. , is independent of the particular ...
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Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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 given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero
Bibliographic information
| Title | Linear Operators, Part 2 Linear Operators, Jacob T. Schwartz Volume 7 of Pure and applied mathematics |
| Authors | Nelson Dunford, Jacob T. Schwartz |
| Publisher | Interscience Publishers, 1982 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0471869139, 9780471869139 |
| Export Citation | BiBTeX EndNote RefMan |