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 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 ƒ is analytic ...
... 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 ƒ is analytic ...
Page 230
... analytic in z - zor , so that the singularity at z = zo is removable . If a , = 0 for p≤0 , zo is called a zero of ... analytic on a domain U in the space of n complex variables , and let g be an analytic function defined on a do- main ...
... analytic in z - zor , so that the singularity at z = zo is removable . If a , = 0 for p≤0 , zo is called a zero of ... analytic on a domain U in the space of n complex variables , and let g be an analytic function defined on a do- main ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ