## Linear Operators: Spectral theory |

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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 in...

Page 1323

To

we have the n jump conditions and the ... and (yo) are uniquely

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

To

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

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

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 T1 and T, ... Let the eigenvalues**determined**bythe periodic boundary conditions stated above be enumerated in increasing

order, and ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 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 Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero