Linear Operators: Spectral theory |
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Page 1290
40 ) is formally self adjoint provided only that the coefficients Pi are real . In the
same way , the ... Then the leading coefficient in t * is ( - 1 ) " ān ; thus , if n is even
, an is real , while if n is odd , an is pure imaginary . If n is even , then tı = ( d / dt ) ...
40 ) is formally self adjoint provided only that the coefficients Pi are real . In the
same way , the ... Then the leading coefficient in t * is ( - 1 ) " ān ; thus , if n is even
, an is real , while if n is odd , an is pure imaginary . If n is even , then tı = ( d / dt ) ...
Page 1486
Equations with periodic coefficients ( which are fundamental in the quantum -
mechanical theory of solid crystals ) have a ... Let t have the form m idli 2 a , ( 1 ) (
) , and suppose that all the coefficients a ; are periodic and have the same period
.
Equations with periodic coefficients ( which are fundamental in the quantum -
mechanical theory of solid crystals ) have a ... Let t have the form m idli 2 a , ( 1 ) (
) , and suppose that all the coefficients a ; are periodic and have the same period
.
Page 1730
For partial differential operators in R with coefficients belonging to C ( R ) , we
may state the following analogue of the Gårding inequality , Lemma 10 . As to its
proof , we need only remark that since , as has been pointed out above , only the
...
For partial differential operators in R with coefficients belonging to C ( R ) , we
may state the following analogue of the Gårding inequality , Lemma 10 . As to its
proof , we need only remark that since , as has been pointed out above , only the
...
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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