## Linear Operators: Spectral theory |

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Page 950

Instead of restricting our consideration to the case of the additive group of real numbers , we shall discuss the case of a locally

Instead of restricting our consideration to the case of the additive group of real numbers , we shall discuss the case of a locally

**compact**Abelian group which we denote by R. We assume throughout that R is o -**compact**, i.e. , the ...Page 1150

ence of Haar measure on a locally

ence of Haar measure on a locally

**compact**, o -**compact**Abelian group . As remarked in the text , the development presented in this section is valid for a general non - discrete locally**compact**, o -**compact**Abelian group .Page 1331

To complete the proof it is therefore sufficient to show that every integral operator in L2 ( 1 ) defined by a kernel K with || K || 2 = $ , $ , 1K ( t , 8 ) / 2 dsdt < 0 is

To complete the proof it is therefore sufficient to show that every integral operator in L2 ( 1 ) defined by a kernel K with || K || 2 = $ , $ , 1K ( t , 8 ) / 2 dsdt < 0 is

**compact**. This is a special case of Exercise VI.9.52 ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Miscellaneous Applications | 937 |

Compact Groups | 945 |

Copyright | |

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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 singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero