## Linear Operators, Part 1 |

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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 230

If no 20 is The largest number n such that a_inl # 0 is called the order of the pole

ар with p < 0 is non - zero , and if we put f ( 20 ) = do , then f becomes

- zo ! < r , so that the singularity at z = removable . If an o for p = 0 , 2 , is called a ...

If no 20 is The largest number n such that a_inl # 0 is called the order of the pole

ар with p < 0 is non - zero , and if we put f ( 20 ) = do , then f becomes

**analytic**in z- zo ! < r , so that the singularity at z = removable . If an o for p = 0 , 2 , is called a ...

Page 586

Nelson Dunford, Jacob T. Schwartz. Then there exists a 8 > 0 such that if \ ul < d ,

then Ū CO ( T ( u ) ) and R ( 2 ; T ( u ) ) is an

PROOF . By Lemma 3 , there is a & such that if sul < 81 , then U CO ( T ( u ) ) .

Nelson Dunford, Jacob T. Schwartz. Then there exists a 8 > 0 such that if \ ul < d ,

then Ū CO ( T ( u ) ) and R ( 2 ; T ( u ) ) is an

**analytic**function of u for each 1 € U.PROOF . By Lemma 3 , there is a & such that if sul < 81 , then U CO ( T ( u ) ) .

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### Contents

Preliminary Concepts | 1 |

The VitaliHahnSaks Theorem and Spaces of Measures | 7 |

B Topological Preliminaries | 10 |

Copyright | |

87 other sections not shown

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