## Linear Operators: Spectral theory |

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Page 853

While there are some isolated discussions of nonselfadjoint operators , such as

that giving the completeness of the generalized eigenfunctions of Hilbert -

Schmidt operators in

the ...

While there are some isolated discussions of nonselfadjoint operators , such as

that giving the completeness of the generalized eigenfunctions of Hilbert -

Schmidt operators in

**Section**XI . 6 , the general theory of spectral operators andthe ...

Page 1270

These rather intricate problems are treated in

of the first half of this

also discussed in Stone [ 3 ; Chap . IX ] . The method used here , however , is

much ...

These rather intricate problems are treated in

**Section**4 . The principal theoremsof the first half of this

**section**are essentially due to von Neumann [ 7 ] and arealso discussed in Stone [ 3 ; Chap . IX ] . The method used here , however , is

much ...

Page 1634

For this reason , we shall devote the next

notational conventions and abbreviations which will be of considerable use in the

...

For this reason , we shall devote the next

**section**to the statement of a series ofnotational conventions and abbreviations which will be of considerable use in the

**sections**to follow . In the body of our analysis ( as in the elementary proof of local...

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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