## Linear Operators: Spectral theory |

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Page 1218

If the

sets 6, with X. gu(),) < e 2 and such that the

Thus ...

If the

**restrictions**fo, gö are continuous then so is the**restriction**... Clearly the**restriction**of X, to the complement of o-6 is continuous. ... Now for n > 2 there aresets 6, with X. gu(),) < e 2 and such that the

**restriction**of f, to 0, is continuous.Thus ...

Page 1239

Conversely, let T be a self adjoint extension of T. Then by Lemma 26, T, is the

linearly independent boundary conditions B, (a) = 0, i = 1,..., k, and we have only

to ...

Conversely, let T be a self adjoint extension of T. Then by Lemma 26, T, is the

**restriction**of To to a subspace Q3 of Q(T*) determined by a symmetric family oflinearly independent boundary conditions B, (a) = 0, i = 1,..., k, and we have only

to ...

Page 1613

A

definition to all functions which satisfy a ... the remaining part of the spectrum

depends on the

the point ...

A

**restriction**of the operator Ti(r, 3:) is obtained by restricting the domain ofdefinition to all functions which satisfy a ... the remaining part of the spectrum

depends on the

**restriction**chosen, and may lie in the residual spectrum and/orthe point ...

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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