## Linear Operators: Spectral theory |

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Page 1379

Let T , T , 4 , 01 , ... , Om , etc. , be as in

functions 0,7 ; ( ) of

be extended to analytic functions defined on the whole neighborhood U of A , 01 ,

... , 0 ...

Let T , T , 4 , 01 , ... , Om , etc. , be as in

**Theorem**18 . Then if , for j > k , thefunctions 0,7 ; ( ) of

**Theorem**18 ( or , the functions 07 ; ( 2 ) of**Theorem**18 ) maybe extended to analytic functions defined on the whole neighborhood U of A , 01 ,

... , 0 ...

Page 1591

The defining property used by them coincides with the property we have given in

extensive use of Definition 1 , has also been used by Šnol [ 1 ] and Naīmark [ 5 ] ...

The defining property used by them coincides with the property we have given in

**Theorem**4. The development followed in this section and the next , which makesextensive use of Definition 1 , has also been used by Šnol [ 1 ] and Naīmark [ 5 ] ...

Page 1904

... IV.15 Alexandroff

space of measurable functions , IV.11.2-3 ( 332–333 ) Egoroff

and ...

... IV.15 Alexandroff

**theorem**on convergence of measures , IV.9.15 ( 316 ) Arzelā**theorem**continuous limits , IV.6.11 ( 268 ) Banach**theorem**for operators intospace of measurable functions , IV.11.2-3 ( 332–333 ) Egoroff

**theorem**on a.e.and ...

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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