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 Z1 , . , Zn . 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 Z1 , . , Zn . 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 230
... analytic in z - z 。< r , so that the singularity at z = zo is 0 for p ≤ 0 , % is called a zero of f ; thus zo is a ... 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 - z 。< r , so that the singularity at z = zo is 0 for p ≤ 0 , % is called a zero of f ; thus zo is a ... 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 converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f 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 S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ