## 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

Conversely , if o is in the Li - closed linear manifold

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

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 jumpequations and by the boundary conditions defining T . Proof . We have seen in

the ...

Page 1323

To

numbers ai ( t ) and Bi ( t ) we have the n jump ... By symmetry ( Vis ) and ( s ) are

also

( 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 | |

15 other sections not shown

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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