## Linear Operators: Spectral operators |

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Page 2300

Then , since the collection of

Then , since the collection of

**finite**sums of projections Ean ; T ' ) is uniformly bounded , it is clear from [ * ] that the collection of**finite**sums of projections Elun ; T + P ) , n 2 K , is uniformly bounded .Page 2333

Hence , in view of the Fubini theorem , the proof of ( a ) will be complete as soon as the quantity f ( t ) f ( s ) e - mte - msf ( t ) f ( s ) dt ds dm = • dt ds t + 8 Lo Lo sio " 0 is proved to be

Hence , in view of the Fubini theorem , the proof of ( a ) will be complete as soon as the quantity f ( t ) f ( s ) e - mte - msf ( t ) f ( s ) dt ds dm = • dt ds t + 8 Lo Lo sio " 0 is proved to be

**finite**.Page 2441

This shows that there exists a

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