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

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Page 1020

( ais ) be the

, 0 , 0 ] , ... , On [ 0 , 0 , 1 ] . Let Ais denote the cofactor of the element dis , i.e. , A ij

is ( -1 ) : + times the determinant of the ( n - 1 ) ( n - 1 )

...

( ais ) be the

**matrix**of an operator A in En relative to the orthonormal basis 81 ( 1, 0 , 0 ] , ... , On [ 0 , 0 , 1 ] . Let Ais denote the cofactor of the element dis , i.e. , A ij

is ( -1 ) : + times the determinant of the ( n - 1 ) ( n - 1 )

**matrix**obtained by deleting...

Page 1275

Jacobi

problem made in Section 8 can be carried considerably ... An infinite

} , j , k 2 0 , is said to be a Jacobi

.

Jacobi

**Matrices**and the Moment Problem The investigations of the momentproblem made in Section 8 can be carried considerably ... An infinite

**matrix**{ azk} , j , k 2 0 , is said to be a Jacobi

**matrix**if ape ар , all p , q , ( i ) ( ii ) apa Ip - 91 > 1.

Page 1338

Let { Mis } be a positive

respect to a positive o - finite measure kl . If the

defined by the equations Mijle ) S.am mij ( 2 ) u ( da ) , where e is any bounded

Borel ...

Let { Mis } be a positive

**matrix**measure whose elements Mis are continuous withrespect to a positive o - finite measure kl . If the

**matrix**of densities { mi ; } isdefined by the equations Mijle ) S.am mij ( 2 ) u ( da ) , where e is any bounded

Borel ...

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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