## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 80

Page 995

Let h be in L ( R ) with himo ) ( = 1 and h : vanishing on an open set

Let h be in L ( R ) with himo ) ( = 1 and h : vanishing on an open set

**containing**the remainder of olt * ) . It follows from Lemma 12 that the set ( h * f * ° )**contains**at most the single point m , and hence , from Theorem 16 and Lemma ...Page 996

From Lemma 12 ( b ) it is seen that olf * ) Cole ) and from Lemma 12 ( c ) and the equation if = tf it follows that olf * q )

From Lemma 12 ( b ) it is seen that olf * ) Cole ) and from Lemma 12 ( c ) and the equation if = tf it follows that olf * q )

**contains**no interior point of o ( q ) . Hence of * v ) is a closed subset of the boundary of o ( q ) .Page 1397

The method of proof is the following : it will be shown that if the theorem is false , then a proper symmetric extension T , of T can be constructed whose domain properly

The method of proof is the following : it will be shown that if the theorem is false , then a proper symmetric extension T , of T can be constructed whose domain properly

**contains**both D ( T ) and the null - space of T * .### What people are saying - Write a review

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

### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

46 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 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 satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero