## Linear Operators: Spectral theory |

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Results 1-3 of 72

Page 990

A bounded measurable function p on R is in the Li-closed linear subspace of L. (

R) which is

Conversely, if p is in the Li-closed linear manifold

A bounded measurable function p on R is in the Li-closed linear subspace of L. (

R) which is

**determined**by the characters in any neighborhood of its spectral set.Conversely, if p is in the Li-closed linear manifold

**determined**by the characters ...Page 1323

To

we have the n jump conditions and the ... Thus (y,y) and (y,) are uniquely

1,..., ot.

To

**determine**the u”--v" = (p++q*)–(u”--v") = (n+k”)–(u"+v”) numbers o,(t) and B, (t)we have the n jump conditions and the ... Thus (y,y) and (y,) are uniquely

**determined**by the jump conditions and by the boundary conditions E*(K) = 0, i =1,..., ot.

Page 1497

Then by Theorems XII.4.28, 4.1, and 4.2, these sets of boundary conditions

the periodic boundary conditions stated above be enumerated in increasing

order, and ...

Then by Theorems XII.4.28, 4.1, and 4.2, these sets of boundary conditions

**determine**self adjoint operators T, and T, ... Let the eigenvalues**determined**bythe periodic boundary conditions stated above be enumerated in increasing

order, and ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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 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 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