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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