## Linear Operators: General theory |

### From inside the book

Results 1-3 of 67

Page 224

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

complex valued

values in X is said to be

derivatives af Əzi ...

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

complex valued

**analytic**functions of one ... A function defined on G and withvalues in X is said to be

**analytic**on G if f is continuous and the first partialderivatives af Əzi ...

Page 229

A function f

( x ) = Σ α , ( α - α ) » , p =which converges uniformly and absolutely in every

annulus a te 32—20 ) SB - ɛ with ε > 0. The coefficients a , are given by the

formulas ...

A function f

**analytic**in an annulus a < 2-20 < B has a unique Laurent expansion f( x ) = Σ α , ( α - α ) » , p =which converges uniformly and absolutely in every

annulus a te 32—20 ) SB - ɛ with ε > 0. The coefficients a , are given by the

formulas ...

Page 230

Nelson Dunford, Jacob T. Schwartz. 20 is The largest number n such that a_ini +

0 is called the order of the pole 2o . If no a , with p < 0 is non - zero , and if we put

| ( 20 ) = do , then f becomes

Nelson Dunford, Jacob T. Schwartz. 20 is The largest number n such that a_ini +

0 is called the order of the pole 2o . If no a , with p < 0 is non - zero , and if we put

| ( 20 ) = do , then f becomes

**analytic**in 12—201 < r , so that the singularity at z ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Preliminary Concepts 1 1 Preliminary Concepts | 1 |

B Topological Preliminaries 10 B Topological Preliminaries | 10 |

Metric Spaces | 18 |

Copyright | |

80 other sections not shown

### Other editions - View all

### Common terms and phrases

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