## Linear Operators: Spectral theory |

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Page 937

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle.

CHAPTER XI Miscellaneous Applications This chapter is devoted to applications

of the spectral

mathematics .

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle.

CHAPTER XI Miscellaneous Applications This chapter is devoted to applications

of the spectral

**theory**of normal operators to problems in a variety of fields ofmathematics .

Page 1583

The researches of Sturm and Liouville were followed by a great deal of work in

the

, the “ spectral ”

decade ...

The researches of Sturm and Liouville were followed by a great deal of work in

the

**theory**of special functions , which we shall briefly touch upon later . However, the “ spectral ”

**theory**which they had discovered was to wait until the firstdecade ...

Page 1634

On the other hand , the ultrahyperbolic operator [ * ] and the puzzling operator [ *

* ] are both well within the terra incognita of today ' s

the basic elementary expression ( 1 ) makes clear , the mere notation for partial ...

On the other hand , the ultrahyperbolic operator [ * ] and the puzzling operator [ *

* ] are both well within the terra incognita of today ' s

**theory**. As the complexity ofthe basic elementary expression ( 1 ) makes clear , the mere notation for partial ...

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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