## Linear Operators: Spectral operators |

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Page 1986

By considering the integral as an iterated integral , it is seen that it suffices to

lim Ś q ( s – t ) dt , t - 0 and so equation ( 5 ) may be

xv .

By considering the integral as an iterated integral , it is seen that it suffices to

**establish**( 5 ) in the case N = 1 . ... sin als – u ) q ( u ) du a- > 00 TTJSU 1 sin atlim Ś q ( s – t ) dt , t - 0 and so equation ( 5 ) may be

**established**by 1986 XV.11.1xv .

Page 2212

We next

fé ... We now

Thus if f ( a ) = f ( a ) on 0 , = ow , equation ( ix ) will be

may ...

We next

**establish**the equation ( viii ) fFz = f Xo ( F ) , FEB . To prove this , let g =fé ... We now

**establish**the relation ( ix ) f ( a ) = fya ) , λεσ , σ ,. To prove ( ix ) it ...Thus if f ( a ) = f ( a ) on 0 , = ow , equation ( ix ) will be

**established**. Hence wemay ...

Page 2234

Then F ( UK - 1 ( n ) = 1 also . Let x be in E ( e ) X and let x be in Dif ( TE ( e ) x ) ) .

Then by Definition 8 , since ( ii ) has already been

sets with closures contained in U , f ( T | E ( e ) X ) x = lim f ( T | F ( en ) E ( e ) X ) ...

Then F ( UK - 1 ( n ) = 1 also . Let x be in E ( e ) X and let x be in Dif ( TE ( e ) x ) ) .

Then by Definition 8 , since ( ii ) has already been

**established**for bounded Borelsets with closures contained in U , f ( T | E ( e ) X ) x = lim f ( T | F ( en ) E ( e ) X ) ...

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### Contents

SPECTRAL OPERATORS 1937 1941 1945 XV Spectral Operators | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

32 other sections not shown

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