Linear Operators: Spectral theory |
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Page 898
If we put E ( d ) = 0 ) when d n ( T ) is void , then Corollary 4 follows immediately
from Theorem 1 and Corollary IX . 3 . 15 . Q . E . D . 5 DEFINITION . The uniquely
defined spectral measure associated , in Corollary 4 , with the normal operator T
...
If we put E ( d ) = 0 ) when d n ( T ) is void , then Corollary 4 follows immediately
from Theorem 1 and Corollary IX . 3 . 15 . Q . E . D . 5 DEFINITION . The uniquely
defined spectral measure associated , in Corollary 4 , with the normal operator T
...
Page 1142
14 . Q . E . D . In what follows , we will use the symbols p and n to denote the
continuous extension to the classes C , of operators of the mappings p and n of
the previous lemma . We will also write t = ( tn ) / 2 . We note the following
corollary .
14 . Q . E . D . In what follows , we will use the symbols p and n to denote the
continuous extension to the classes C , of operators of the mappings p and n of
the previous lemma . We will also write t = ( tn ) / 2 . We note the following
corollary .
Page 1301
Proceeding inductively we see that v6k ) ( b ) = 0 , 0 Sk 5 2n - 1 . However , as vo
satisfies an equation of order 2n , v , must be identically zero . This contradiction
completes the proof . Q . E . D . 23 COROLLARY . Let T be a formal differential ...
Proceeding inductively we see that v6k ) ( b ) = 0 , 0 Sk 5 2n - 1 . However , as vo
satisfies an equation of order 2n , v , must be identically zero . This contradiction
completes the proof . Q . E . D . 23 COROLLARY . Let T be a formal differential ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
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