## Linear Operators: Spectral theory |

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Page 1239

Conversely, let T be a self

restriction of To to a subspace Q3 of Q(T*) determined by a symmetric family of

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 therestriction of To to a subspace Q3 of Q(T*) determined by a symmetric family of

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

to ...

Page 1270

The problem of determining whether a given symmetric operator has a self

affirmative, it is important to know what the self

how they ...

The problem of determining whether a given symmetric operator has a self

**adjoint extension**is of crucial importance in ... If the answer to this problem isaffirmative, it is important to know what the self

**adjoint extensions**look like andhow they ...

Page 1622

Borg showed that, given the distribution of eigenvalues for two self

, and proved that the distribution of eigenvalues of one self

Borg showed that, given the distribution of eigenvalues for two self

**adjoint****extensions**of the operator d \? - - - - t), ... Levinson [4] simplified Borg's arguments, and proved that the distribution of eigenvalues of one self

**adjoint extension**...### What people are saying - Write a review

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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