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

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Page 955

The letter M will

be the isometric isomorphism of A onto C ( M ) whose existence is asserted by

Corollary IX.3.8 . For fin L ( R ) , we usually write t ( T1 ) simply as tf . The letter E

will ...

The letter M will

**denote**the space of maximal ideals of A , and t : A + C ( M ) willbe the isometric isomorphism of A onto C ( M ) whose existence is asserted by

Corollary IX.3.8 . For fin L ( R ) , we usually write t ( T1 ) simply as tf . The letter E

will ...

Page 1126

of the closed set C ; we shall

C ) . Since each projection in the spectral resolution of T and hence each

continuous function of T is a strong limit of linear combinations of the projections

Ei , it ...

of the closed set C ; we shall

**denote**this subspace of L [ 0 , 1 ] by the symbol L , (C ) . Since each projection in the spectral resolution of T and hence each

continuous function of T is a strong limit of linear combinations of the projections

Ei , it ...

Page 1486

In the next few paragraphs t

operator of ordern , defined on the interval R = { - 00 < t < +00 } . Let t have the

form dii T = Ža , ( 6 ) dt j = 0 and suppose that all the coefficients a , are periodic

and ...

In the next few paragraphs t

**denotes**a formally self adjoint formal differentialoperator of ordern , defined on the interval R = { - 00 < t < +00 } . Let t have the

form dii T = Ža , ( 6 ) dt j = 0 and suppose that all the coefficients a , are periodic

and ...

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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

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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