## Linear Operators: Spectral theory |

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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

a ' resentations as an Le - space and in this setting the class of

a ' resentations as an Le - space and in this setting the class of

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

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. If K is a

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. If K is a

**Hilbert**-**Schmidt**operator in L2 ( A ) , there exists a unique set Kj ( s , t ) of kernels representing K in the sense that ( 3 ) K11 ( s ) , 12 ( s ) , .### What people are saying - Write a review

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### Contents

8 | 876 |

859 | 885 |

extensive presentation of applications of the spectral theorem | 911 |

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### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume 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 domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero