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

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Page 1338

Let { uis } be a positive matrix measure whose elements Mis are continuous with

Let { uis } be a positive matrix measure whose elements Mis are continuous with

**respect**to a positive o - finite measure u . If the matrix of densities { m } is defined by the equations His ( e ) = S.m , ( ) u ( da ) , Mijle ) where e ...Page 1340

Let ů be another o - finite positive regular measure with

Let ů be another o - finite positive regular measure with

**respect**to which the set functions Mij are continuous . Let mj } be the corresponding matrix of densities , and let { n } be the matrix of densities of the with**respect**to the ...Page 1359

Let и be positive o - finite measure with

Let и be positive o - finite measure with

**respect**to which all the set functions Pij are continuous and let m be the Radon - Nikodým derivative of Pij with**respect**to u . If f is in D ( T ) CL ( I ) , then the integral mij n Sf 3 m ...### 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 Ly(R 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 unique unit unitary vanishes vector zero