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

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Page 930

This

Section XI.4 . A similar

find all of the closed in variant subspaces for the operator of multiplication by z on

...

This

**problem**is related to the**problem**of spectral synthesis to be discussed inSection XI.4 . A similar

**problem**was discussed by Beurling [ 4 ] , who was able tofind all of the closed in variant subspaces for the operator of multiplication by z on

...

Page 1250

In general , st " u ( dt ) is called the nth moment with respect to the origin and the

) which has prescribed moments . The Hamburger moment

In general , st " u ( dt ) is called the nth moment with respect to the origin and the

**problem**proposed and solved by Stieltjes is to find a mass distribution u on ( 0 , 0) which has prescribed moments . The Hamburger moment

**problem**is similar to ...Page 1270

The

adjoint extension is of crucial importance in determining whether the spectral

theorem may be employed . If the answer to this

important to ...

The

**problem**of determining whether a given symmetric operator has a selfadjoint extension is of crucial importance in determining whether the spectral

theorem may be employed . If the answer to this

**problem**is affirmative , it isimportant to ...

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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