Linear Operators: General theory |
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Page 224
... analytic functions of a complex variable to the case where the func- tions are vector valued . It will be assumed that the reader is familiar with the elementary theory of complex valued analytic functions of one complex variable and ...
... analytic functions of a complex variable to the case where the func- tions are vector valued . It will be assumed that the reader is familiar with the elementary theory of complex valued analytic functions of one complex variable and ...
Page 228
... analytic on an open set U in the space of the complex variables 21 , .. , n . Let V be a bounded open subset of U whose closure is contained in U. If fn converges at each point of U to a function f on U then f is analytic in U , and the ...
... analytic on an open set U in the space of the complex variables 21 , .. , n . Let V be a bounded open subset of U whose closure is contained in U. If fn converges at each point of U to a function f on U then f is analytic in U , and the ...
Page 229
... analytic function in this annulus and the series is the Laurent expansion of its sum . This annulus is the largest annulus with center Zo in which an analytic function with the given Laurent expan- sion can be analytic . + ∞ If f is ...
... analytic function in this annulus and the series is the Laurent expansion of its sum . This annulus is the largest annulus with center Zo in which an analytic function with the given Laurent expan- sion can be analytic . + ∞ If f is ...
Contents
Exercises | 9 |
Definitions and Basic Properties | 13 |
Metric Spaces | 19 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence closed sets compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense disjoint Doklady Akad E₁ elements ergodic exists f₁ finite number follows function defined function f Hausdorff space Hence Hilbert space homomorphism integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose Theorem theory topological space u-integrable u-measurable u-null uniformly unit sphere vector space weakly compact zero ΕΕΣ