## Linear Operators: General theory |

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Page 224

Functions of a Complex Variable In some of the chapters to follow , and especially in Chapter VII , we shall use extensions of certain well - known results in the theory of

Functions of a Complex Variable In some of the chapters to follow , and especially in Chapter VII , we shall use extensions of certain well - known results in the theory of

**analytic**functions of a complex variable to the case where the ...Page 228

Un of a collection of open sets in the complex plane , and C is a continuous rectifiable curve lying wholly in Un , then the function g defined by 21 Zn is

Un of a collection of open sets in the complex plane , and C is a continuous rectifiable curve lying wholly in Un , then the function g defined by 21 Zn is

**analytic**in U , X ... Un - 1 : If f is**analytic**in a neighborhood of the closure ...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 every annulus atɛ $ 2-20 SB - ɛ with a > 0. The coefficients a , are given by ...### 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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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