## Linear Operators: Spectral theory |

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Page 1297

Q.E.D. We now turn to a discussion of the specific form assumed in the present

case by the abstract "

see that the discussion leads us to a number of results about deficiency indices .

Q.E.D. We now turn to a discussion of the specific form assumed in the present

case by the abstract "

**boundary values**” introduced in the last chapter . We shallsee that the discussion leads us to a number of results about deficiency indices .

Page 1307

, D , are

functional A defined by the formula A ( f ) = Alf ) is also a

**boundary values**C1 , C2 , D1 , D , where C1 , C , are**boundary values**at a and D, D , are

**boundary values**at b , such ... formation of complex conjugates , so thefunctional A defined by the formula A ( f ) = Alf ) is also a

**boundary value**for t .Page 1471

Oi , Oly real , , y real , if 1 has no

tat , g ) - ( 1 , 728 ; = D. ( 1 ) D2 ( g ) – D2 ( 1 ) D , ( g ) – F. ( 1 , g ) , f , geD ( T ( 12 )

) ...

Oi , Oly real , , y real , if 1 has no

**boundary values**at b ; while if t has**boundary****values**at b , we may find two real**boundary values**D ,, D , for T , at b , such that (tat , g ) - ( 1 , 728 ; = D. ( 1 ) D2 ( g ) – D2 ( 1 ) D , ( g ) – F. ( 1 , g ) , f , geD ( T ( 12 )

) ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 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