## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 990

A bounded measurable function qon R is in the Ly - closed linear subspace of Lo

( R ) which is

. Conversely , if y is in the Ly - closed linear manifold

A bounded measurable function qon 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 y is in the Ly - closed linear manifold

**determined**by the ...Page 1323

To

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

are also

conditions Ez ( K ) ...

To

**determine**the u * + 3 * = ( p * + q * ) - ( u * + v * ) = ( n + k * ) - ( 4 * + v * )numbers ai ( t ) and Bi ( t ) we have the n jump ... By symmetry ( Vis ) and ( Vis )

are also

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

Page 1497

Then by Theorems XII.4.28 , 4.1 , and 4.2 , these sets of boundary conditions

periodic boundary conditions stated above be enumerated in increasing order ,

and ...

Then by Theorems XII.4.28 , 4.1 , and 4.2 , these sets of boundary conditions

**determine**self adjoint operators T ... Let the eigenvalues**determined**by theperiodic boundary conditions stated above be enumerated in increasing order ,

and ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

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### Common terms and phrases

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 Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero