## Linear Operators: Spectral theory |

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Page 1009

Schmidt type will be developed and rather deep and fundamental completeness

theorems for the eigenfunctions of such operators and associated unbounded ...

**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 Lg - space and in this setting the class of

space H . A bounded linear operator T is said to be a

case ...

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

**HilbertSchmidt****operators**may be defined as follows . ... complete orthonormal set in the Hilbertspace H . A bounded linear operator T is said to be a

**Hilbert**-**Schmidt operator**incase ...

Page 1132

Nelson Dunford, Jacob T. Schwartz. If K is a

there exists a unique set Kij ( s , t ) of kernels representing K in the sense that K [

11 ( s ) , fa ( s ) , . . . ] = [ gi ( s ) , ge ( s ) , . . . ] ( 3 ) where 1 ( 4 ) 8 : ( 8 ) = K ; ( s , t )

...

Nelson Dunford, Jacob T. Schwartz. If K is a

**Hilbert**-**Schmidt operator**in LZ ( A ) ,there exists a unique set Kij ( s , t ) of kernels representing K in the sense that K [

11 ( s ) , fa ( s ) , . . . ] = [ gi ( s ) , ge ( s ) , . . . ] ( 3 ) where 1 ( 4 ) 8 : ( 8 ) = K ; ( s , t )

...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint operator Akad algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero