## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1145

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

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

**representations**of compact groups . ... Then a**representation**R of G in X is a strongly continuous homomorphism g → R ( g ) of G into the group of bounded invertible linear ...Page 1146

Any finite dimensional

Any finite dimensional

**representation**of a compact group G is a direct sum of irreducible**representations**. This theorem shows that in studying finite dimensional**representations**of a compact group G we may , without loss of generality ...Page 1217

A spectral

A spectral

**representation**of a Hilbert space H onto - L2 ( un ) relative to a self adjoint operator T in H is said to be an ordered**representation**of H relative to T. The measure u is called the measure of the ordered**representation**.### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

additive adjoint operator 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