## Linear Operators: Spectral theory |

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Page 1297

We shall also be able to locate

points of the interval , and to represent

form . The fundamental definitions are as follows : 17 DEFINITION . Let T be a

formal ...

We shall also be able to locate

**boundary values**at one or another of the endpoints of the interval , and to represent

**boundary values**in a concrete analyticalform . The fundamental definitions are as follows : 17 DEFINITION . Let T be a

formal ...

Page 1307

, , D , are

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

**boundary values**C1 , C2 , D2 , D , where C1 , C , are**boundary values**at a and D, , D , are

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

**boundary value**for t .Page 1471

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. if t has no

...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. if t has no

**boundary values**at b ; while if has**boundary values**at b , we may find two real**boundary values**D1 , D , for T , at b , such that ( tzt , g ) - ( 1 , T28 ) = D ( ) D2 ( g )...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 869 |

Commutative BAlgebras | 877 |

Copyright | |

39 other sections not shown

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### Common terms and phrases

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