## Linear Operators: Spectral theory |

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Jacobi

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

said to be a Jacobi

Jacobi

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

**matrix**{ a } x } , j , k 2 0 , issaid to be a Jacobi

**matrix**if ( 1 ) Apa = āap , Apa = 0 , all p , q , $ p - 91 > 1 .Page 1338

Let { uis } be a positive

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

defined by the equations Migle ) = S . m . , ( 2 ) u ( da ) , where e is any bounded

Borel ...

Let { uis } be a positive

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

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

Borel ...

Page 1378

= 1 , . . . , k ; Pij = 0 , if i > k or ; > k . ... i > k or j > k , we get a

which by Corollary 21 must be the same as the

**matrix**measure { fis } , i , j = 1 , . . . , k of Theorem 23 is unique , and Pis = Pis , i , j= 1 , . . . , k ; Pij = 0 , if i > k or ; > k . ... i > k or j > k , we get a

**matrix**measure { Pij }which by Corollary 21 must be the same as the

**matrix**measure of Theorem 13 .### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

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additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero