## Linear Operators: Part III: Spectral Operators [by] Nelson Dunford and Jacob T. Schwartz, with the Assistance of William G. Bade and Robert G. Bartle, Volume 1 |

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Page 2103

This Wiener theorem and P. Lévy's generalization

This Wiener theorem and P. Lévy's generalization

**obtained**by replacing 1/2 by any function f ( a ) analytic for l in a neighborhood of the spectrum of the element a in A , are extensions of the results to be found in IX.4.10 and IX.4.11 ...Page 2176

He has

He has

**obtained**generalizations of the results of this chapter , as well as analogous theorems . CHAPTER XVII Algebras of Spectral Operators 1. Introduction The sum 2176 XVI.8 XVI . SPECTRAL OPERATORS : SUFFICIENT CONDITIONS.Page 2405

The same conclusion is readily

The same conclusion is readily

**obtained**in the extreme case r = 00 ; we leave it to the reader to give the necessary details . Next let 1 sr $ 2 . Let hy be a second non - negative , u - measurable function defined on S. Then we ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

28 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 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