## Linear Operators: Spectral theory |

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Page 1145

The Peter-Weyl Theorem 1.4 is basic to the theory of

groups. The principal definitions and theorems of this theory are as follows.

DEFINItion: Let G be a topological group, and 3: a B-space. Then a

The Peter-Weyl Theorem 1.4 is basic to the theory of

**representations**of compactgroups. The principal definitions and theorems of this theory are as follows.

DEFINItion: Let G be a topological group, and 3: a B-space. Then a

**representation**R ...Page 1146

Any finite dimensional

irreducible

dimensional

generality, confine ...

Any finite dimensional

**representation**of a compact group G is a direct sum ofirreducible

**representations**. This theorem shows that in studying finitedimensional

**representations**of a compact group G we may, without loss ofgenerality, confine ...

Page 1217

A spectral

adjoint operator T in § is said to be an ordered

The measure u is called the measure of the ordered

A spectral

**representation**of a Hilbert space $5 onto X.1. L2(u,) relative to a selfadjoint operator T in § is said to be an ordered

**representation**of $5 relative to T.The measure u is called the measure of the ordered

**representation**. The sets e ...### What people are saying - Write a review

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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