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 = z 。 is removable . If a , = 0 for p ≤ 0 , zo is called a zero ... 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 = z 。 is removable . If a , = 0 for p ≤ 0 , zo is called a zero ... 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 ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear functional linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite 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 theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ