## Linear Operators: General theory |

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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 229

A function f

A function f

**analytic**in an annulus « < 12-20 < B has a unique Laurent expansion a , ( 3 - ) ” , 1 ар which converges uniformly and absolutely in every annulus ata 52-2 B - with a > 0. The coefficients a , are given by the formulas ta ) ...Page 588

Consequently , it is possible to solve for the tij , and obtain in each case the quotient of an

Consequently , it is possible to solve for the tij , and obtain in each case the quotient of an

**analytic**function by 4 ( u ) . Since , for lul < 82 , the function 4 ( u ) # 0 , its reciprocal , and therefore each tij , is**analytic**.### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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