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

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Page 1020

9 0 ij ( a ;; ) be the

9 0 ij ( a ;; ) be the

**matrix**of an operator A in E “ relative to the orthonormal basis di = ( 1 , 0 , ... , 0 ] , ... , On = [ 0 , ... , 0 , 1 ] . Let Ai , denote the [ cofactor of the element aij , i.e. , Aig is ( -1 ) ' + i times the ...Page 1275

Jacobi

Jacobi

**Matrices**and the Moment Problem The investigations of the moment problem made in Section 8 can be carried ... An infinite**matrix**{ a ; k } , j , k 2 0 , is said to be a Jacobi**matrix**if apa = āaps all p , q , ( i ) ( ii ) 9 Ip ...Page 1338

Let { uis } be a positive

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 ...### 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