## Linear Operators: General theory |

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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 229

These facts , as well as the following remarks about Laurent series may all be

proved by the standard arguments used for complex functions . A function f

ap ( z ...

These facts , as well as the following remarks about Laurent series may all be

proved by the standard arguments used for complex functions . A function f

**analytic**in an annulus « < 12— % ! < B has a unique Laurent expansion f ( x ) = {ap ( z ...

Page 230

Nelson Dunford, Jacob T. Schwartz, William G. Bade. 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, William G. Bade. 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 ...### What people are saying - Write a review

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

### Common terms and phrases

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 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