## Linear Operators: Spectral theory |

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Page 1185

CHAPTER XII

preceding chapter we have seen how the spectral theory developed in Chapters

IX and X may be applied to various problems in mathematical analysis . However

, we ...

CHAPTER XII

**Unbounded**Operators in Hilbert Space 1. Introduction In thepreceding chapter we have seen how the spectral theory developed in Chapters

IX and X may be applied to various problems in mathematical analysis . However

, we ...

Page 1268

The first significant advance towards the analysis of

operators was made , in 1923 , by Carleman ( 1 ) in his study of singular integral

equations . However , it was several years later that von Neumann [ 8 ] , in 1927 ...

The first significant advance towards the analysis of

**unbounded**symmetricoperators was made , in 1923 , by Carleman ( 1 ) in his study of singular integral

equations . However , it was several years later that von Neumann [ 8 ] , in 1927 ...

Page 1278

The study of these operators is complicated by the fact that they are necessarily

operator is by no means trivial ; the study of symmetric

The study of these operators is complicated by the fact that they are necessarily

**unbounded**. Consequently , the problem of choosing a domain for a differentialoperator is by no means trivial ; the study of symmetric

**unbounded**operators in ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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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 neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero