## Linear Operators: Spectral Theory : Self Adjoint Operators in Hilbert Space, Volume 2 |

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Results 1-3 of 65

Page 2286

If A is the closed densely defined linear map of X into the Hilbert space H of

Lemma 35 , then the closure of AQA - 1 is a bounded normal operator . For each

bounded Borel function g on the plane let Š ( g )

1 .

If A is the closed densely defined linear map of X into the Hilbert space H of

Lemma 35 , then the closure of AQA - 1 is a bounded normal operator . For each

bounded Borel function g on the plane let Š ( g )

**denote**the closure of AS ( 9 ) A -1 .

Page 2320

n - 1 1 = 0 ( 2 ) Throughout this section , Bi , i = 1 , . . . , n , will

linearly independent boundary values for 7 . Thus , by Corollary XIII . 2 . 23 , there

exist two n x n matrices dij and Buy such that ( 1 ) B ( A ) = 3 & 1 . 454540 ) + Buf ...

n - 1 1 = 0 ( 2 ) Throughout this section , Bi , i = 1 , . . . , n , will

**denote**a set of nlinearly independent boundary values for 7 . Thus , by Corollary XIII . 2 . 23 , there

exist two n x n matrices dij and Buy such that ( 1 ) B ( A ) = 3 & 1 . 454540 ) + Buf ...

Page 2436

Next , let C . ( En )

valued functions defined in En and vanishing outside a bounded set , let g € Co (

En ) , and let g = f , with f e L2 ( En ) , so that , by the Plancherel theorem ( XV . 11

.

Next , let C . ( En )

**denote**the set of all infinitely often differentiable complexvalued functions defined in En and vanishing outside a bounded set , let g € Co (

En ) , and let g = f , with f e L2 ( En ) , so that , by the Plancherel theorem ( XV . 11

.

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### Contents

SPECTRAL OPERATORS XV Spectral Operators | 1924 |

Introduction | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

32 other sections not shown

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