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 |
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Page 2391
Thus , if de R , 191 a I pl > & a , and A ( ) # 0 , then ( W1 - T ) -1 = R ( ; T ) exists and equals R ( A ) , a completing the proof of the present lemma . Q.E.D. 5 COROLLARY . Let the hypotheses of Lemma 4 be satisfied and let 0 < ...
Thus , if de R , 191 a I pl > & a , and A ( ) # 0 , then ( W1 - T ) -1 = R ( ; T ) exists and equals R ( A ) , a completing the proof of the present lemma . Q.E.D. 5 COROLLARY . Let the hypotheses of Lemma 4 be satisfied and let 0 < ...
Page 2395
The function oz ( t , x ) ) ) -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 ...
The function oz ( t , x ) ) ) -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 ...
Page 2396
214 ( s I e " g ( e ) del It follows from this formula just as in the proof of Lemma 1 ( cf. the paragraph following formula ( 14 ) ) that lim 18+ ( 0 ) = 0 , uniformly for 0 St < 0 . 141-00 HEP + Hence , by formula ( 24 ) of the proof ...
214 ( s I e " g ( e ) del It follows from this formula just as in the proof of Lemma 1 ( cf. the paragraph following formula ( 14 ) ) that lim 18+ ( 0 ) = 0 , uniformly for 0 St < 0 . 141-00 HEP + Hence , by formula ( 24 ) of the proof ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
47 other sections not shown
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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 defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension 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 |