## 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

on G and with values in X is said to be

partial ...

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

complex valued

**analytic**functions of one complex variable ... A function f definedon G and with values in X is said to be

**analytic**on G if f is continuous and the firstpartial ...

Page 228

XUn 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 8 ( 22 , . . . , Zn

- 1 ) = [ c1 ( 72 , . . . , Zn ) dzn is

XUn 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 8 ( 22 , . . . , Zn

- 1 ) = [ c1 ( 72 , . . . , Zn ) dzn is

**analytic**in U , X . . . Un - 1 . If f is**analytic**in a ...Page 230

Nelson Dunford. The largest number n such that a _ ini + 0 is called the order of

the pole Zo . If no a , with p < 0 is non - zero , and if we put f ( 20 ) = do , then f

becomes

Nelson Dunford. The largest number n such that a _ ini + 0 is called the order of

the pole Zo . If no a , with p < 0 is non - zero , and if we put f ( 20 ) = do , then f

becomes

**analytic**in 3 — 2o < r , so that the singularity at z = zo is removable .### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect 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