## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

### From inside the book

Results 1-3 of 70

Page 2017

and the fraction in the

2 ) * + 1681 $ * } 1/2 which is bounded on all of R " . Thus As has a resolution of

the identity . Furthermore , the set S , is the null set { 8 | 8 = 82 = 0 } , so that As is

...

and the fraction in the

**inequality**( i ) of Theorem 6 is Isi - sl2 + 2 | 818212 { ( si - $2 ) * + 1681 $ * } 1/2 which is bounded on all of R " . Thus As has a resolution of

the identity . Furthermore , the set S , is the null set { 8 | 8 = 82 = 0 } , so that As is

...

Page 2190

Thus for some constant K we have | S ( f ) | SK \ f | and to prove the final

of the present theorem it will suffice to prove that lifle = S ( f ) . Since both terms in

this

Thus for some constant K we have | S ( f ) | SK \ f | and to prove the final

**inequality**of the present theorem it will suffice to prove that lifle = S ( f ) . Since both terms in

this

**inequality**are continuous functions of f , it will suffice to prove it for every ...Page 2399

By ( 44 ) and Hölder's

din " " skal v 4. ) 29/1 Isla . The

and ( 45 ) . Since the

...

By ( 44 ) and Hölder's

**inequality**we have ( 45 ) { 1 * 10 * \ ve ) — ( $ * $ \ ( ) ? dudin " " skal v 4. ) 29/1 Isla . The

**inequality**( 42a ) follows immediately from ( 43 )and ( 45 ) . Since the

**inequality**( 42b ) may be deduced in a precisely similar way...

### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 other sections not shown

### Other editions - View all

### Common terms and phrases

adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding defined Definition denote dense determined differential operator discrete domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero