## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

### From inside the book

Results 1-3 of 38

Page 2063

... S is the one point compactification of N - dimensional Euclidean space RN and

e is the self adjoint spectral measure given in equation ( 11 . 15 ) . We know from

Lemma 9 . 2 that if the elements a , A in A , AP ,

... S is the one point compactification of N - dimensional Euclidean space RN and

e is the self adjoint spectral measure given in equation ( 11 . 15 ) . We know from

Lemma 9 . 2 that if the elements a , A in A , AP ,

**respectively**, possess bounded ...Page 2108

Let u (

in order for there to exist a necessarily unique spectral measure d on the Baire

sets in X X Y to A such that 1 ( 8 X 0 ) = u ( d ) v ( o ) for all 8 , o , it is necessary ...

Let u (

**respectively**, v ) be a spectral measure on X (**respectively**, Y ) to A . Thenin order for there to exist a necessarily unique spectral measure d on the Baire

sets in X X Y to A such that 1 ( 8 X 0 ) = u ( d ) v ( o ) for all 8 , o , it is necessary ...

Page 2109

( c ) The mappings u → - d u / dta + tzu on the spaces 0 (

rapidly decreasing Co functions (

real line are scalar . Thus the Fourier transform u ( t ) → SR e - 2a itsu ( s ) ds ...

( c ) The mappings u → - d u / dta + tzu on the spaces 0 (

**respectively**, Tl ) ofrapidly decreasing Co functions (

**respectively**, tempered distributions ) on thereal line are scalar . Thus the Fourier transform u ( t ) → SR e - 2a itsu ( s ) ds ...

### 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 | |

28 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 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