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

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Page 984

The set of functions f in L ( R ) for which f vanishes in a neighborhood of infinity is

in L2 ( R , B , u ) which vanish outside of compact sets is

The set of functions f in L ( R ) for which f vanishes in a neighborhood of infinity is

**dense**in Ly ( R ) . PROOF . It follows from Lemma 3.6 that the set of all functionsin L2 ( R , B , u ) which vanish outside of compact sets is

**dense**in this space ...Page 1246

Self Adjoint Operators in Hilbert Space. Spectral theory. Part II Nelson Dunford,

Jacob T. Schwartz. We may also regard A as a mapping from the

subspace D ( T ) of H into the space Hı . In this case A is still continuous , for | Axli

= ( Ax ...

Self Adjoint Operators in Hilbert Space. Spectral theory. Part II Nelson Dunford,

Jacob T. Schwartz. We may also regard A as a mapping from the

**dense**subspace D ( T ) of H into the space Hı . In this case A is still continuous , for | Axli

= ( Ax ...

Page 1905

... ( 233 ) Deficiency indices and spaces , definition , XII.4.9 ( 1226 ) De Morgan ,

rules of , ( 2 )

41 ( 438–439 )

functions ...

... ( 233 ) Deficiency indices and spaces , definition , XII.4.9 ( 1226 ) De Morgan ,

rules of , ( 2 )

**Dense**convex sets , V.7.27 ( 437 )**Dense**linear manifolds , V.7.40-41 ( 438–439 )

**Dense**set , definition , 1.6.11 ( 21 ) density of continuousfunctions ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

### 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