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 2381
Now define oi ( t , x ) to be the unique solution of ( T - u ? ) o = 0 , ( t , u ) [ 0 , 0 ) < Pt , which coincides with gu ( t ) for t 2 a . ( cf. Corollary XIII.1.5 ) . If S is some other positive constant and 8 < , then ag 2 Qe .
Now define oi ( t , x ) to be the unique solution of ( T - u ? ) o = 0 , ( t , u ) [ 0 , 0 ) < Pt , which coincides with gu ( t ) for t 2 a . ( cf. Corollary XIII.1.5 ) . If S is some other positive constant and 8 < , then ag 2 Qe .
Page 2391
For use in what is to follow we record the formula for R ( a ; T ) obtained in the proof of Lemma 4 and also observe that in constructing the kernel R ( s , t ; d ) in Lemma 4 we may replace the particular “ second solution ” oz ( t ...
For use in what is to follow we record the formula for R ( a ; T ) obtained in the proof of Lemma 4 and also observe that in constructing the kernel R ( s , t ; d ) in Lemma 4 we may replace the particular “ second solution ” oz ( t ...
Page 2394
λσ a - solutions ởi = gilt , -u ( a ) ) and on = oit , u ( a ) ) of the equation to = do . ... Then there exists a solution og ( t , ) of the equation to ru'o , defined for 0 St < oo and oz , u = for all sufficiently small ue P + ...
λσ a - solutions ởi = gilt , -u ( a ) ) and on = oit , u ( a ) ) of the equation to = do . ... Then there exists a solution og ( t , ) of the equation to ru'o , defined for 0 St < oo and oz , u = for all sufficiently small ue P + ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
31 other sections not shown
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