## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 80

Page 1425

It follows from the

It follows from the

**preceding**lemma that there exists a constant k such that for all t in [ a , o ) , [ * ] k max \ ( s ) ass Stm max \ f ' ( s ) . ass Stm Indeed , if this were not the case , then to every integer m we could associate ...Page 1437

it follows immediately from the

it follows immediately from the

**preceding**lemma that 20 € 0 ( T ( T ) ) , so that by Definition 6.1 , 2o eo ( t ) . Conversely , let 20 € 0 , ( t ) . Let D be the closure in the Hilbert space D ( T1 ( T ) ) of D ( To ( T ) ) , and let ...Page 1771

Theorem 6.23 ) satisfies the hypotheses of statement ( ii ) of the

Theorem 6.23 ) satisfies the hypotheses of statement ( ii ) of the

**preceding**theorem . Q.E.D. I APPENDIX Hilbert space is a linear vector space H XIV.8.2 1771 PARABOLIC EQUATIONS AND SEMI - GROUPS.### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

57 other sections not shown

### Other editions - View all

### 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 complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure 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