## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1642

Let I , be the bounded open

such that U , K , = 1 .. Using Lemma 1 , let { w } be a sequence of functions in C (

1. ) ...

Let I , be the bounded open

**subset**of I where Im ( x ) + 0. Since 1 , is an open**subset**of E " , there exists an increasing sequence { K , } of compact**subsets**of 1 ,such that U , K , = 1 .. Using Lemma 1 , let { w } be a sequence of functions in C (

1. ) ...

Page 1650

which y vanishes . ... Let F be a distribution in the open

closed set Cp in I which is the complement in I of the largest open set in I in which

...

**subsets**of I and let F be in D ( I ) . ... Let K be a compact**subset**of Ual , outside ofwhich y vanishes . ... Let F be a distribution in the open

**subset**I of En . Then theclosed set Cp in I which is the complement in I of the largest open set in I in which

...

Page 1669

Let M : 1 -1 , be a mapping of I , into I , such that ( a ) M - ' C is a compact

I , whenever C is a compact

Then ( i ) for each q in Co ( 12 ) , po M will denote the function y in CR ( 1 . ) ...

Let M : 1 -1 , be a mapping of I , into I , such that ( a ) M - ' C is a compact

**subset**ofI , whenever C is a compact

**subset**of Iz ; ( b ) ( M ( :) ) , € CR ( 1 ) , j = 1 , ... , No.Then ( i ) for each q in Co ( 12 ) , po M will denote the function y in CR ( 1 . ) ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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