## Linear Operators: Spectral theory |

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Page 940

The unique measure whose existence is established in Theorem 1 is called the

Haar measure on the compact group G. By using Haar measure it will be shown

that the class of continuous functions on G which are

The unique measure whose existence is established in Theorem 1 is called the

Haar measure on the compact group G. By using Haar measure it will be shown

that the class of continuous functions on G which are

**finite dimensional**in the ...Page 1092

Let Q be a

of To; suppose that the dimension of 3 is d. Then, plainly, & is invariant under T

and T*, and, since (T&", w) = (3*, Toa.) = 0 for all a, we have T&H = 0 and similarly

...

Let Q be a

**finite**-**dimensional**space including both the range of T and the rangeof To; suppose that the dimension of 3 is d. Then, plainly, & is invariant under T

and T*, and, since (T&", w) = (3*, Toa.) = 0 for all a, we have T&H = 0 and similarly

...

Page 1146

M. Any

irreducible representations. This theorem shows that in studying

generality, ...

M. Any

**finite dimensional**representation of a compact group G is a direct sum ofirreducible representations. This theorem shows that in studying

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

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 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 adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero