## Linear Operators: General theory |

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Page 224

It will be assumed that the reader is familiar with the elementary theory of complex valued

It will be assumed that the reader is familiar with the elementary theory of complex valued

**analytic**functions of one complex variable and this theory will ...Page 228

Un - 1 : If f is

Un - 1 : If f is

**analytic**in a neighborhood of the closure of the bounded open set U which is bounded by a finite collection B of closed ...Page 229

A function

A function

**analytic**in an annulus . < 2-20 < B has a unique Laurent expansion f ( x ) E ap ( 2—20 ) " , co p = 0 which converges uniformly and absolutely in ...### What people are saying - Write a review

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero