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

### From inside the book

Results 1-3 of 76

Page 2108

143 ] used the word “ spectral ” ) if there

measure u on X to A and a bounded Baire measurable function f : X TMC such

that a = S f ( x ) p ( dx ) . It follows that there

on a ...

143 ] used the word “ spectral ” ) if there

**exists**a compact space X , a spectralmeasure u on X to A and a bounded Baire measurable function f : X TMC such

that a = S f ( x ) p ( dx ) . It follows that there

**exists**a spectral measure va definedon a ...

Page 2405

... eldr ) . s ' s S S If he L , ( S , £ , y ) and 2 Sr < oo , it follows that the integral ( 14 )

( Ah ) ( 8 ) = S 14 ( 8 , 0 ) | ( 0 ) u ( dt )

, for the norm of an element f of L , ( S , E , p ) , we have | Ah , S { A } , \ h \ , .

... eldr ) . s ' s S S If he L , ( S , £ , y ) and 2 Sr < oo , it follows that the integral ( 14 )

( Ah ) ( 8 ) = S 14 ( 8 , 0 ) | ( 0 ) u ( dt )

**exists**for u - almost all s , and that , writing fl, for the norm of an element f of L , ( S , E , p ) , we have | Ah , S { A } , \ h \ , .

Page 2418

, the integral ( 74 ) 514 , 62 " , 2 ) { S , 43120 | 15 ( 2 ) | dx dy ] dx dy DOD

for almost all z " e D . Therefore , by Tonelli ' s theorem ( III . 11 . 14 ) , the integral

...

**exists**almost everywhere for each fe Īp ( D , Y ) , and , using Lemma 5 once more, the integral ( 74 ) 514 , 62 " , 2 ) { S , 43120 | 15 ( 2 ) | dx dy ] dx dy DOD

**exists**for almost all z " e D . Therefore , by Tonelli ' s theorem ( III . 11 . 14 ) , the integral

...

### What people are saying - Write a review

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

### Other editions - View all

### Common terms and phrases

adjoint operator analytic applications arbitrary assumed B-space Banach space belongs Boolean algebra Borel sets boundary bounded bounded operator Chapter clear closed commuting compact complex condition consider constant contained continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established example exists extension fact finite follows formula given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear linear operator manifold Math Moreover multiplicity norm normal perturbation plane positive preceding present problem projections PROOF properties proved range regular resolution resolvent respectively restriction Russian satisfies scalar type seen sequence shown shows similar spectral measure spectral operator spectrum subset subspace sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector weakly zero