## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 82

Page 1239

Conversely , let T , be a self adjoint

restriction of T * to a subspace W of D ( T * ) determined by a symmetric family of

linearly independent boundary conditions B ; ( x ) = 0 , i = 1 , . . . , k , and we ...

Conversely , let T , be a self adjoint

**extension**of T . Then by Lemma 26 , T , is therestriction of T * to a subspace W of D ( T * ) determined by a symmetric family of

linearly independent boundary conditions B ; ( x ) = 0 , i = 1 , . . . , k , and we ...

Page 1270

symmetric operator has a self adjoint

determining whether the spectral theorem may be employed . If the answer to this

...

**Extensions**of symmetric operators . The problem of determining whether a givensymmetric operator has a self adjoint

**extension**is of crucial importance indetermining whether the spectral theorem may be employed . If the answer to this

...

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

particular

boundary ...

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 theparticular

**extension**chosen , i . e . , is independent of the particular set ofboundary ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

### Other editions - View all

### Common terms and phrases

additive adjoint operator 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 function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero