Linear Operators: Spectral theory |
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Page 1142
The validity of the present theorem in the range 1 < p S2 now follows at once from
its validity in the range 2 Sp oo and from Lemma 9 . 14 . Q . E . D . In what follows
, we will use the symbols p and n to denote the continuous extension to the ...
The validity of the present theorem in the range 1 < p S2 now follows at once from
its validity in the range 2 Sp oo and from Lemma 9 . 14 . Q . E . D . In what follows
, we will use the symbols p and n to denote the continuous extension to the ...
Page 1684
Hence , it is quite sufficient to prove the present lemma for the special case m = 0
. By Corollary 2 again , each derivative g of order 1 of F belongs to Lp ( Em ) ( and
has compact carrier ) , for every p ' satisfying the inequality ( i ) 1 1 ( k - 1 ) p ...
Hence , it is quite sufficient to prove the present lemma for the special case m = 0
. By Corollary 2 again , each derivative g of order 1 of F belongs to Lp ( Em ) ( and
has compact carrier ) , for every p ' satisfying the inequality ( i ) 1 1 ( k - 1 ) p ...
Page 1703
In the present section it will be seen that it can , at least for the class of elliptic
partial differential operators to be defined below . A crucial theorem in the
development of the theory of Chapter XIII was Theorem XIII . 2 . 10 , which was
based on ...
In the present section it will be seen that it can , at least for the class of elliptic
partial differential operators to be defined below . A crucial theorem in the
development of the theory of Chapter XIII was Theorem XIII . 2 . 10 , which was
based on ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
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