## Linear Operators: Spectral operators |

### From inside the book

Results 1-3 of 75

Page 1976

Let the operator A in AP have the property ( i ) sup e - ess sup ( E ( o ; Â ( s ) ) < 00 . σε SES Then for every bounded Borel scalar function o defined on the spectrum o ( A ) , the

Let the operator A in AP have the property ( i ) sup e - ess sup ( E ( o ; Â ( s ) ) < 00 . σε SES Then for every bounded Borel scalar function o defined on the spectrum o ( A ) , the

**integral**( ii ) Sow , P [ A ] E ( d ) ; Â ( 3 ) ) is ...Page 1990

Here , we shall first be concerned with certain special examples of convolutions which map H into H , which belong to the algebra A , and which have an

Here , we shall first be concerned with certain special examples of convolutions which map H into H , which belong to the algebra A , and which have an

**integral**representation in one of the two forms ( 18 ) ( f * ° ) ( 8 ) = Sex 918 — 1 ...Page 1991

The

The

**integral**( 20 ) is thus defined for bounded continuous H valued functions on RN and , in particular , if f ( t ) = Q2 , for some q in H. The**integral**in ( 19 ) is defined to be the**integral**( 20 ) . It is clear that if for almost ...### What people are saying - Write a review

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

### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 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 countably additive defined Definition denote dense determined differential operator 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