## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 76

Page 937

However, due to the comprehensiveness and power of the general spectral

but also to develop their principal results, and this we shall attempt to do. The

topics ...

However, due to the comprehensiveness and power of the general spectral

**theory**, it is possible not only to give a satisfactory foundation for these subjects,but also to develop their principal results, and this we shall attempt to do. The

topics ...

Page 1583

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

the

the “spectral”

of ...

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 first decadeof ...

Page 1634

On the other hand, the ultrahyperbolic operator [+] and the puzzling operator [+o]

are both well within the terra incognita of today's

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

On the other hand, the ultrahyperbolic operator [+] and the puzzling operator [+o]

are both well within the terra incognita of today's

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

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 measure multiplicity 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