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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 ...
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 ...
Page 225
These integrals may be defined as follows : Let I = { tsa St b } be an interval of the
real axis and let a be a complex valued function which is defined , continuous
and of bounded variation on 1 . Then a is the parametrization of a continuous ...
These integrals may be defined as follows : Let I = { tsa St b } be an interval of the
real axis and let a be a complex valued function which is defined , continuous
and of bounded variation on 1 . Then a is the parametrization of a continuous ...
Page 238
With the one exception of Hilbert space , each of them will consist of real or
complex valued functions f , g defined on a specified domain S . Here , addition
and multiplication are understood to be defined in the natural way , i . e . , by the ...
With the one exception of Hilbert space , each of them will consist of real or
complex valued functions f , g defined on a specified domain S . Here , addition
and multiplication are understood to be defined in the natural way , i . e . , by the ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional 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 neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero