## Linear Operators: Spectral theory |

### From inside the book

Results 1-3 of 88

Page 891

scalar

chapter we shall only integrate bounded

discussion of the integral will be restricted to that case. Let X be a field of subsets

of a set ...

scalar

**function**f with respect to the operator valued set**function**E. In the presentchapter we shall only integrate bounded

**functions**f and so the followingdiscussion of the integral will be restricted to that case. Let X be a field of subsets

of a set ...

Page 1178

It is plain from Plancherel's theorem that % is a bounded mapping of the space

Le of scalar-valued

maps the vector-valued

g,($) ...

It is plain from Plancherel's theorem that % is a bounded mapping of the space

Le of scalar-valued

**functions**into the ... Let ~/ be the mapping in L,(la) whichmaps the vector-valued

**function**whose nth component has the Fourier transformg,($) ...

Page 1922

Total space of functionals, definition, V.3.1 (418) Total variation of a

5.15 (140) of a set

2.2 (4) Trace, of a finite matrix, VI.9.28 (515), XI.6.8 (1016) of a matrix, definition, ...

Total space of functionals, definition, V.3.1 (418) Total variation of a

**function**, III.5.15 (140) of a set

**function**, III.1.4 (97). (See also Variation) Totally ordered set, I.2.2 (4) Trace, of a finite matrix, VI.9.28 (515), XI.6.8 (1016) of a matrix, definition, ...

### What people are saying - Write a review

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

### 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