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

### From inside the book

Results 1-3 of 85

Page 2391

Thus , if de R , 191 > € , and A ( a ) # 0 , then ( AI – T ) - 1 = R ( 2 ; T ) exists and

equals R ( a ) , completing the proof of the present

COROLLARY . Let the hypotheses of

Suppose in the ...

Thus , if de R , 191 > € , and A ( a ) # 0 , then ( AI – T ) - 1 = R ( 2 ; T ) exists and

equals R ( a ) , completing the proof of the present

**lemma**. Q . E . D . 5COROLLARY . Let the hypotheses of

**Lemma**4 be satisfied and let 0 < l , < .Suppose in the ...

Page 2395

The function oz ( t , u ( a ) ) = - 2iuốz ( t , u ( a ) ) therefore satisfies the conditions

of the present

be satisfied , and in particular let A + ( a ) and A - ( a ) be non - vanishing for 0 si ...

The function oz ( t , u ( a ) ) = - 2iuốz ( t , u ( a ) ) therefore satisfies the conditions

of the present

**lemma**. Q . E . D . 9 COROLLARY . Let the hypotheses of**Lemma**7be satisfied , and in particular let A + ( a ) and A - ( a ) be non - vanishing for 0 si ...

Page 2396

It follows from this formula just as in the proof of

following formula ( 14 ) ) that lim \ f ( t ) = 0 , uniformly for ost < . 14100 HEP +

Hence , by formula ( 24 ) of the proof of

- tufu ...

It follows from this formula just as in the proof of

**Lemma**1 ( cf . the paragraphfollowing formula ( 14 ) ) that lim \ f ( t ) = 0 , uniformly for ost < . 14100 HEP +

Hence , by formula ( 24 ) of the proof of

**Lemma**3 , Qu ( t ) ~ e - ttu ; su ( t ) = – jue- tufu ...

### 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