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

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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 || \ 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 || \ is

**compact**. This is a special case of Exercise VI.9.52 , but , for the sake of completeness , a proof ...### What people are saying - Write a review

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