## Linear Operators: Spectral operators |

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Page 1986

Hence , F is a continuous map of into Ø . We next

( 5 ) . Once this is ... plus duļat 1 po sin als – u ) TT - 00 $ - U - q ( u ) du at = lim S

916 – ) sing at at , and so equation ( 5 ) may be

Hence , F is a continuous map of into Ø . We next

**establish**the inversion formula( 5 ) . Once this is ... plus duļat 1 po sin als – u ) TT - 00 $ - U - q ( u ) du at = lim S

916 – ) sing at at , and so equation ( 5 ) may be

**established**by 1986 XV . 11 .Page 2212

We next

Xocp ) so that , using ( vii ) , we have g ( a ) = 0 for 1€ 0 , 0 ( F ) = Oft · Also T ( g )

Fx = T ( f2 ) T ( Xo « p » ) Fx = FT ( fr ) x = FAx = A Fx . Thus statement ( vi ) , with f

...

We next

**establish**the equation fre = f : Xocp ) , Fe B . To prove this , let g = f :Xocp ) so that , using ( vii ) , we have g ( a ) = 0 for 1€ 0 , 0 ( F ) = Oft · Also T ( g )

Fx = T ( f2 ) T ( Xo « p » ) Fx = FT ( fr ) x = FAx = A Fx . Thus statement ( vi ) , with f

...

Page 2234

Then F ( UTM - 1 ( n ) = I also . Let x be in E ( e ) X and let x be in Dif ( T | E ( e ) x )

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

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

) ...

Then F ( UTM - 1 ( n ) = I also . Let x be in E ( e ) X and let x be in Dif ( T | E ( e ) x )

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

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

) ...

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### Contents

SPECTRAL OPERATORS | 1924 |

An Operational Calculus for Bounded Spectral | 1941 |

Part | 1950 |

Copyright | |

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