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 analytic functions of a complex variable to the case where the ...
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 ...
Page 228
Let V be a bounded open subset of U whose closure is contained in U. If in converges at each point of U to a function f on U then f is analytic in U , and the partial derivatives of in of arbitrarily large order converge to the ...
Let V be a bounded open subset of U whose closure is contained in U. If in converges at each point of U to a function f on U then f is analytic in U , and the partial derivatives of in of arbitrarily large order converge to the ...
Page 230
20 of n The largest number n such that a_ini # 0 is called the order of the pole 20 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 = 2 ...
20 of n The largest number n such that a_ini # 0 is called the order of the pole 20 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 = 2 ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero