## 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 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 the functions are ...Page 228

Let Vbe a bounded open subset of U whose closure is contained in V. If /„

converges at each point of V to a function f on U then f is

partial derivatives of fn of arbitrarily large order converge to the corresponding

partial ...

Let Vbe a bounded open subset of U whose closure is contained in V. If /„

converges at each point of V to a function f on U then f is

**analytic**in U, and thepartial derivatives of fn of arbitrarily large order converge to the corresponding

partial ...

Page 230

The largest number n such that a_ln\ ^ 0 is called the order of the pole Zq. If no ap

with p < 0 is non-zero, and if we put /(z0) = a0, then / becomes

< r, so that the singularity at z = Zq is removable. If av = 0 for p Si 0, z0 is called ...

The largest number n such that a_ln\ ^ 0 is called the order of the pole Zq. If no ap

with p < 0 is non-zero, and if we put /(z0) = a0, then / becomes

**analytic**in \z— z0|< r, so that the singularity at z = Zq is removable. If av = 0 for p Si 0, z0 is called ...

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

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