## Linear Operators: Spectral theory |

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Page 853

4 , as an appended section on Hilbert space immediately following

This appended ... Thus , for the reader who is familiar with the contents of

I . An ...

4 , as an appended section on Hilbert space immediately following

**Chapter**XIV .This appended ... Thus , for the reader who is familiar with the contents of

**Chapters**I , II , III , and VII , there will be only occasional need for reference to PartI . An ...

Page 887

Preliminary Notions The spectral theorem to be proved in this

introduce a theory which parallels in Hilbert space the thcory in n - dimensional

unitary ...

**CHAPTER**X Bounded Normal Operators in Hilbert Space 1 . Terminology andPreliminary Notions The spectral theorem to be proved in this

**chapter**willintroduce a theory which parallels in Hilbert space the thcory in n - dimensional

unitary ...

Page 1185

preceding

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

...

**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

...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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