## 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 1930

If & is a Boolean algebra of subsets of the complex

If & is a Boolean algebra of subsets of the complex

**plane**which contains the void set and the whole**plane**, in short , if is a field of sets in the complex**plane**, then a spectral measure E on E is called a resolution of the identity ...Page 2043

The semi - group S ( t ) has a strongly analytic extension to a semi - group 8 ( 5 ) defined for $ in the half

The semi - group S ( t ) has a strongly analytic extension to a semi - group 8 ( 5 ) defined for $ in the half

**plane**R ( S ) > 0 . The unique solution to the Cauchy problem presented by the equations ( ii ) , ( iii ) , ( iv ) is ...Page 2087

... infinitesimal generator of a strongly continuous semi - group s ( t ) , t 20 , of bounded linear operators in HP and S ( t ) has a strongly analytic extension to a semi - group S ( $ ) defined for Ğ in the half

... infinitesimal generator of a strongly continuous semi - group s ( t ) , t 20 , of bounded linear operators in HP and S ( t ) has a strongly analytic extension to a semi - group S ( $ ) defined for Ğ in the half

**plane**R ( S ) > 0 .### 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