## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 990

A bounded measurable function q on R is in the Ly - closed linear subspace of Lo ( R ) which is

A bounded measurable function q on R is in the Ly - closed linear subspace of Lo ( 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 ...Page 1321

The matrices I = ( y ) and I " = ( yi ) in the preceding theorem are uniquely

The matrices I = ( y ) and I " = ( yi ) 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 az ( t ) ...Page 1323

To

To

**determine**the u * + u * = ( p * + q * ) - ( u * + v * ) = ( n + k * ) - ( u * + v * ) numbers ai ( t ) and Bi ( t ) ... By symmetry ( 11 ) and ( Vás ) are also**determined**uniquely by the jump conditions and the boundary conditions E ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

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 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero