## Linear Operators: General theory |

### From inside the book

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Page 224

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 ...

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 thefunctions ...

Page 228

Un 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 ( 71 , . . , % n

- 1 ) = Schlža , . . . , Zn ) dzn is

Un 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 ( 71 , . . , % n

- 1 ) = Schlža , . . . , Zn ) dzn is

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

Nelson Dunford, Jacob T. Schwartz. The largest number n such that a _ in ! # 0 is

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

20 ) = 2g , then f becomes

Nelson Dunford, Jacob T. Schwartz. The largest number n such that a _ in ! # 0 is

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

20 ) = 2g , then f becomes

**analytic**in z - - 20 < r , so that the singularity at z = zo ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

21 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex Consequently constant contains converges convex Corollary defined DEFINITION denote dense determined differential 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 mean measure space metric neighborhood norm positive measure problem Proc projection PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement strongly subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero