## 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 1931

If x is a vector in X , then by an

If x is a vector in X , then by an

**analytic**extension of R ( É ; T ' ) x will be meant an X - valued function f defined and**analytic**on an open set D ( S ) 2 p ( T ) and such that ( ŠI – T ) f ( $ ) = x , & € D ( f ) .Page 1932

In this case x ( $ ) is a single valued

In this case x ( $ ) is a single valued

**analytic**function with domain p ( x ) and with X ( ) = R ( E ; T ' ) x , ξε ρ ( T ' ) . It will be shown in the next section that , if T is a spectral operator , the function R ( $ ; T ) x has ...Page 2248

Let f be a function

Let f be a function

**analytic**in a domain U which , when taken together with a finite number of exceptional points p , includes a neighborhood of o ( T ) and a neighborhood of the point at infinity . Suppose that each exceptional point p ...### What people are saying - Write a review

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### Contents

SPECTRAL OPERATORS | 1924 |

Introduction | 1927 |

Terminology and Preliminary Notions | 1929 |

Copyright | |

47 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