## Linear Operators: Spectral operators |

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Page 2108

are , Let u ( respectively , v ) be a spectral measure on X ( respectively , Y ) to A. Then in order for there to

are , Let u ( respectively , v ) be a spectral measure on X ( respectively , Y ) to A. Then in order for there to

**exist**a necessarily unique spectral measure , on the Baire sets in X X Y to A such that a ( 8 x 0 ) = u ( d ) vlo ) for ...Page 2418

**exists**almost everywhere for each fe Î ( D , Y ) , and , using Lemma 5 once more , the integral ( 74 ) 1,1416 " , ** { ! | 14:14 | 156 ) de dybder de**exists**for almost all z " e D. Therefore , by Tonelli's theorem ( III.11.14 ) ...Page 2441

This shows that there

This shows that there

**exists**a finite absolute constant c ' such that I ( 0 ) < c ' ( 1 + 101 ) -n + 1 . Using this inequality and using ( 37 ) , we see that there**exists**a finite constant M " independent of ε such that 22 V4 ( 43 ) 1V4 ...### 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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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