## 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 230

If no 20 is The largest number n such that a_inl # 0 is called the order of the pole ар with p < 0 is non - zero , and if we put f ( 20 ) = do , then f becomes

If no 20 is The largest number n such that a_inl # 0 is called the order of the pole ар with p < 0 is non - zero , and if we put f ( 20 ) = do , then f becomes

**analytic**in z - zo ! < r , so that the singularity at z = removable .Page 586

Then there exists a 8 > 0 such that if \ ul < d , then Ū CO ( T ( u ) ) and R ( 2 ; T ( u ) ) is an

Then there exists a 8 > 0 such that if \ ul < d , then Ū CO ( T ( u ) ) and R ( 2 ; T ( u ) ) is an

**analytic**function of u for each 1 € U. PROOF . By Lemma 3 , there is a & such that if sul < 81 , then U CO ( T ( u ) ) .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

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