## 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

Let V be a bounded open subset of U whose closure is contained in U. If in converges at each point of U to a function f on U then f is

Let V be a bounded open subset of U whose closure is contained in U. If in converges at each point of U to a function f on U then f is

**analytic**in U ...Page 230

Then g is said to be an

Then g is said to be an

**analytic**continuation of i if V contains U properly , if g ( x1 , ... , 2n ) = f ( 21 , ... , Zn ) for every point 21 , · ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

quences | 26 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain 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 mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero