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 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 lemma . Q . E . D . 5
COROLLARY . Let the hypotheses of Lemma 4 be satisfied and let 0 < l , < .
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 . 5
COROLLARY . 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 lemma . Q . E . D . 9 COROLLARY . Let the hypotheses of Lemma 7
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 7
be 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 Lemma 1 ( cf . the paragraph
following 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 ...
It follows from this formula just as in the proof of Lemma 1 ( cf . the paragraph
following 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.
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
Bibliographic information
| Title | 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 Pure and applied mathematics, v. 7 |
| Authors | Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle |
| Editors | L. Bers, J. J. Stoker |
| Publisher | Wiley-Interscience, 1957 |
| Original from | the University of Michigan |
| Digitized | 2 Feb 2010 |
| ISBN | 0471226394, 9780471226390 |
| Length | 667 pages |
| Export Citation | BiBTeX EndNote RefMan |