## Linear Operators: Spectral theory |

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Page 990

A bounded measurable function o on R is in the L - closed linear subspace of L (

R ) which is

Conversely , if y is in the L , - closed linear manifold

A bounded measurable function o on R is in the L - closed linear subspace of L (

R ) which is

**determined**by the characters in any neighborhood of its spectral set .Conversely , if y is in the L , - closed linear manifold

**determined**by the ...Page 1321

The matrices I = ( Vis ) and I ' = ( y ) in the preceding theorem are uniquely

PROOF . We have seen in the derivation of Theorem 8 that the functions ; ( t ) and

Bi ( t ) ...

The matrices I = ( Vis ) and I ' = ( y ) in the preceding theorem are uniquely

**determined**by the jump equations and by the boundary conditions defining T .PROOF . We have seen in the derivation of Theorem 8 that the functions ; ( t ) and

Bi ( t ) ...

Page 1323

To

numbers ai ( t ) and Bi ( t ) we have the n ... By symmetry ( Yus ) and ( Vás ) 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 ... By symmetry ( Yus ) and ( Vás ) are

also

**determined**uniquely by the jump conditions and the boundary conditions Ez( K ) ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

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additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives 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 neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero