## 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

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

**establish**( 5 ) in the case N ... du a- > 00 TTJSU 1 sin at lim Ś q ( s – t ) dt , t - 0 and so equation ( 5 ) may be**established**by 1986 XV.11.1 xv .Page 2212

We next

We next

**establish**the equation ( viii ) fFz = f Xo ( F ) , FEB . ... We now**establish**the relation ( ix ) f ( a ) = fya ) , λεσ , σ ,. ... Thus if f ( a ) = f ( a ) on 0 , = ow , equation ( ix ) will be**established**.Page 2234

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

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

**established**for bounded Borel sets with closures contained in U , f ( T | E ( e ) X ) x = lim f ( T | F ( en ) E ( e ) X ) F ( en ) x no = lim ...### What people are saying - Write a review

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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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### Common terms and phrases

adjoint operator Amer analytic apply arbitrary assumed B-space Banach space belongs Boolean algebra Borel set boundary conditions bounded bounded operator Chapter clear closed commuting compact complex constant contains continuous converges Corollary corresponding countably additive defined Definition denote dense determined differential operator domain elements equation equivalent established exists extension fact finite follows formal formula function given gives Hence Hilbert space hypothesis identity inequality integral invariant inverse Lemma limit linear operator Math Moreover multiplicity norm perturbation plane positive preceding present problem projections PROOF properties prove range resolution resolvent restriction Russian satisfies scalar type seen sequence shown shows similar solution spectral measure spectral operator spectrum subset sufficiently Suppose Theorem theory topology unbounded uniformly unique valued vector zero