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 o ( t , u ) to be the unique solution of ( r - u ? ) o = 0 , ( t , u ) € [ 0 , 0 ) < Pet , which coincides with gult ) for t 2 az ( cf. Corollary XIII.1.5 ) . If S is some other positive constant and S < € , then ag 2 ag .
Now define o ( t , u ) to be the unique solution of ( r - u ? ) o = 0 , ( t , u ) € [ 0 , 0 ) < Pet , which coincides with gult ) for t 2 az ( cf. Corollary XIII.1.5 ) . If S is some other positive constant and S < € , then ag 2 ag .
Page 2384
Q.E.D. For the spectral analysis of the operator T , we shall also need asymptotic information on the “ second solution ” of the differential equation To to = użo , that is , the solution asymptotic to e - tut as t + 00 .
Q.E.D. For the spectral analysis of the operator T , we shall also need asymptotic information on the “ second solution ” of the differential equation To to = użo , that is , the solution asymptotic to e - tut as t + 00 .
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 " ozlt ...
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 " ozlt ...
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Contents
SPECTRAL OPERATORS | 1924 |
Introduction | 1927 |
Terminology and Preliminary Notions | 1929 |
Copyright | |
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