Linear Operators: Spectral theory |
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Page 1027
5 shows that a is an eigenvalue and hence for some non - zero æ in H we have
Tx = ax , and hence , since T = TE , we have ( ET ) ( Ex ) = 1 Ex . Hence a belongs
to the spectrum of ET . Conversely , suppose that a non - zero scalar 1 belongs ...
5 shows that a is an eigenvalue and hence for some non - zero æ in H we have
Tx = ax , and hence , since T = TE , we have ( ET ) ( Ex ) = 1 Ex . Hence a belongs
to the spectrum of ET . Conversely , suppose that a non - zero scalar 1 belongs ...
Page 1116
1 , B belongs to the Hilbert - Schmidt class Cz . If we let Aq ; = ri - P2Pi , then A is
plainly self adjoint and A belongs to the class Cr , where r ( 1 - p / 2 ) = p , i . e . , r
= p ( 1 - p / 2 ) - 1 . Thus , by Lemma 9 , T = BA belongs to the class Cs , where s ...
1 , B belongs to the Hilbert - Schmidt class Cz . If we let Aq ; = ri - P2Pi , then A is
plainly self adjoint and A belongs to the class Cr , where r ( 1 - p / 2 ) = p , i . e . , r
= p ( 1 - p / 2 ) - 1 . Thus , by Lemma 9 , T = BA belongs to the class Cs , where s ...
Page 1684
Then , if every partial derivative of F of order k belongs to L ( Em ) , it follows that
every partial derivative of F of order not more than m is continuous in the closure
of Em . PROOF . By Corollary 2 and Hölder ' s inequality , each ( k - m ) th ...
Then , if every partial derivative of F of order k belongs to L ( Em ) , it follows that
every partial derivative of F of order not more than m is continuous in the closure
of Em . PROOF . By Corollary 2 and Hölder ' s inequality , each ( k - m ) th ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
15 other sections not shown
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