Linear Operators, Part 2 |
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Page 990
A bounded measurable function o on R is in the L -closed linear subspace of LO ( R ) which is determined by the characters in any neighborhood of its spectral set . Conversely , if y is in the Ly - closed linear manifold determined by ...
A bounded measurable function o on R is in the L -closed linear subspace of LO ( R ) which is determined by the characters in any neighborhood of its spectral set . Conversely , if y is in the Ly - closed linear manifold determined by ...
Page 1321
The matrices I = ( y ) and I ' = ( y ) in the Vij ( ) preceding theorem are uniquely determined by the jump equations and by the boundary conditions defining T. - . * 9 PROOF . We have seen in the derivation of Theorem 8 that the ...
The matrices I = ( y ) and I ' = ( y ) in the Vij ( ) preceding theorem are uniquely determined by the jump equations and by the boundary conditions defining T. - . * 9 PROOF . We have seen in the derivation of Theorem 8 that the ...
Page 1323
To determine the u * + v * = ( p * + q * ) - ( 4 * + v * ) + + u * ( n + k * ) - ( u * + v * ) numbers ... Bie Wg . Thus ( Vis ) and ( Vís ) are uniquely determined by the jump conditions and by the boundary conditions E * ( K ) = 0 ...
To determine the u * + v * = ( p * + q * ) - ( 4 * + v * ) + + u * ( n + k * ) - ( u * + v * ) numbers ... Bie Wg . Thus ( Vis ) and ( Vís ) are uniquely determined by the jump conditions and by the boundary conditions E * ( K ) = 0 ...
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Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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 given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero