## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 56

Page 1051

Nelson Dunford, Jacob T. Schwartz. Plenh ( x ) dx PSen f ( x ) dx . Proof .

Statement ( i ) is

consequences of Definition 1 and of the formulae SemP ( x ) dx = Seng ( Ux ) dx ,

Sen ...

Nelson Dunford, Jacob T. Schwartz. Plenh ( x ) dx PSen f ( x ) dx . Proof .

Statement ( i ) is

**evident**from Definition 1. Statements ( ii ) and ( iii ) are**evident**consequences of Definition 1 and of the formulae SemP ( x ) dx = Seng ( Ux ) dx ,

Sen ...

Page 1173

The space L , ( Lp ) may in an

the product set E " XS and the inequality to be proved reduces to ( 41 ) SoS . 2 ( x

- y ) \ x - y " fly , s ) dy dxds En selle SS 1 / ( , 8 ) | Pdrds . This inequality is ...

The space L , ( Lp ) may in an

**evident**manner be identified with the Lo - space onthe product set E " XS and the inequality to be proved reduces to ( 41 ) SoS . 2 ( x

- y ) \ x - y " fly , s ) dy dxds En selle SS 1 / ( , 8 ) | Pdrds . This inequality is ...

Page 1661

The analogs of Lemma 3 and Definition 4 are now

them in the new context we shall simply refer to “ Lemma 3 or Definition 4 as

generalized to D , ( 1 ) ” wherever necessary . 31 DEFINITION . Suppose that I is

an ...

The analogs of Lemma 3 and Definition 4 are now

**evident**, and instead of statingthem in the new context we shall simply refer to “ Lemma 3 or Definition 4 as

generalized to D , ( 1 ) ” wherever necessary . 31 DEFINITION . Suppose that I is

an ...

### What people are saying - Write a review

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

### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

### 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 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