## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 63

Page 889

5 ) , every set in the domain of a spectral measure satisfying ( iii ) is necessarily

an open and closed subset of o ( T ) and ... a spectral measure which is defined

on the Boolean algebra B of all

for ...

5 ) , every set in the domain of a spectral measure satisfying ( iii ) is necessarily

an open and closed subset of o ( T ) and ... a spectral measure which is defined

on the Boolean algebra B of all

**Borel sets**in the plane and which satisfies ( iv )for ...

Page 909

Spectral Representation Let u be a finite positive measure defined on the

S . One of the simplest examples of a bounded normal operator is the operator T

...

Spectral Representation Let u be a finite positive measure defined on the

**Borel****sets**B of the complex plane and vanishing on the complement of a bounded setS . One of the simplest examples of a bounded normal operator is the operator T

...

Page 913

Let E be the spectral resolution for T and let vn ( e ) = ( E ( e ) yn , yn ) for each

0 , and such that if e is a Borel subset of the complement en of en and No v ; ( e )

...

Let E be the spectral resolution for T and let vn ( e ) = ( E ( e ) yn , yn ) for each

**Borel set**e . ... 14 ) , let { en } be a sequence of**Borel sets**such that X = v ; ( en ) =0 , and such that if e is a Borel subset of the complement en of en and No v ; ( e )

...

### 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 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