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

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Page 1162

is isomorphic with the complex field , and it turns out that the

ideals of Ly ( R ) are in one - to - one correspondence with the points of Mo , i.e. ,

with all the maximal ideals of the algebra obtained by adjoining an identity to L (

R ) ...

is isomorphic with the complex field , and it turns out that the

**regular**maximalideals of Ly ( R ) are in one - to - one correspondence with the points of Mo , i.e. ,

with all the maximal ideals of the algebra obtained by adjoining an identity to L (

R ) ...

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The particular solution Fa ( s ) of this equation may be characterized as being

being

...

The particular solution Fa ( s ) of this equation may be characterized as being

**regular**and having the value 1 at zero , and F & ( 18 ) may be characterized asbeing

**regular**and having the value 1 at one . Let F. be the unique solution of the...

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( See Reflexivity )

equation ...

( See Reflexivity )

**Regular**closure , ( 462-463 )**Regular**convexity , ( 462 463 )**Regular**element in a B - algebra , IX.1.2 ( 861 )**Regular**element in a ring , ( 40 )**Regular**method of summability , II.4.35 ( 75 )**Regular**point of a differentialequation ...

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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