Linear Operators: Spectral theory |
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Page 884
The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom
most of the results given in Section 1 are due . ... The proof of this lemma given
here is that given by Arens [ 6 ] , who has also ( Arens [ 7 ] ) obtained this result in
...
The study of ideal theory in B - algebra was inaugurated by Gelfand [ 1 ] to whom
most of the results given in Section 1 are due . ... The proof of this lemma given
here is that given by Arens [ 6 ] , who has also ( Arens [ 7 ] ) obtained this result in
...
Page 1419
Clearly , f has a single minimum f ( mi + 1 ) between Sit1 and 8i + 2 , a single
maximum f ( mi + 2 ) between Si + 2 and Sit3 , etc . We will show that 1 / ( m ; ) | 2 \
| ( mi + 1 ) | 2 \ / ( mi + 2 ) | Z . . . , which will clearly establish the desired result .
Clearly , f has a single minimum f ( mi + 1 ) between Sit1 and 8i + 2 , a single
maximum f ( mi + 2 ) between Si + 2 and Sit3 , etc . We will show that 1 / ( m ; ) | 2 \
| ( mi + 1 ) | 2 \ / ( mi + 2 ) | Z . . . , which will clearly establish the desired result .
Page 1433
In case the indicial equation has two roots which differ by an integer or has
multiple roots , a corresponding result may be stated ; but here the basis for
solutions of [ * ] may have a more complex form , involving logarithmic terms . We
shall not ...
In case the indicial equation has two roots which differ by an integer or has
multiple roots , a corresponding result may be stated ; but here the basis for
solutions of [ * ] may have a more complex form , involving logarithmic terms . We
shall not ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
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additive Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero