Linear Operators: Spectral theory |
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Page 990
A bounded measurable function o on R is in the Ly - closed linear subspace of L (
R ) which is determined by the characters in any neighborhood of its spectral set .
Conversely , if o is in the Li - closed linear manifold determined by the ...
A bounded measurable function o on R is in the Ly - closed linear subspace of L (
R ) which is determined by the characters in any neighborhood of its spectral set .
Conversely , if o is in the Li - closed linear manifold determined by the ...
Page 1321
MICHIGAN LIBRARIES iht UNIVERSITY W 9 COROLLARY . The matrices l ' = ( y
) and I ' = ( vv ) in the preceding theorem are uniquely determined by the jump
equations and by the boundary conditions defining T . Proof . We have seen in
the ...
MICHIGAN LIBRARIES iht UNIVERSITY W 9 COROLLARY . The matrices l ' = ( y
) and I ' = ( vv ) in the preceding theorem are uniquely determined by the jump
equations and by the boundary conditions defining T . Proof . We have seen in
the ...
Page 1323
To determine the u * + v * = ( p * + q * ) - ( u * + v * ) = ( n + k * ) - ( 4 * + v * )
numbers ai ( t ) and Bi ( t ) we have the n jump ... By symmetry ( Vis ) and ( s ) are
also determined uniquely by the jump conditions and the boundary conditions E ;
( K ) ...
To determine the u * + v * = ( p * + q * ) - ( u * + v * ) = ( n + k * ) - ( 4 * + v * )
numbers ai ( t ) and Bi ( t ) we have the n jump ... By symmetry ( Vis ) and ( s ) are
also determined uniquely by the jump conditions and the boundary conditions E ;
( K ) ...
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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