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

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Page 1009

**Hilbert**-**Schmidt**Operators In this section the theory of operators of the**Hilbert**-**Schmidt**type will be developed and rather deep and fundamental completeness theorems for the eigenfunctions of such operators and associated unbounded ...Page 1010

resentations as an Ly - space and in this setting the class of

resentations as an Ly - space and in this setting the class of

**HilbertSchmidt**operators may be defined as follows . a ... orthonormal set in the Hilbert space H. A bounded linear operator T is said to be a**Hilbert**-**Schmidt**operator in ...Page 1132

If K is a

If K is a

**Hilbert**-**Schmidt**operator in L ( A ) , there exists a unique set Kij ( s , t ) of kernels representing K in the sense that ( 3 ) KL ( s ) , 12 ( s ) , ... ] = 8 , ( s ) , g ( s ) , ... ] where ( 4 ) 8 .### 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