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 230
... analytic in 2-2 < r , 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 2-2 < r , 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 ...
Page 586
... analytic function of μ for each λ € U. μ PROOF . By Lemma 3 , there is a d1 such that if │μ ] < d1 , then ŪСo ( T ... analytic , it follows from the general theory of analytic func- tions ( cf. III.14 ) that R ( 2 ; T ( u ) ) is an ...
... analytic function of μ for each λ € U. μ PROOF . By Lemma 3 , there is a d1 such that if │μ ] < d1 , then ŪСo ( T ... analytic , it follows from the general theory of analytic func- tions ( cf. III.14 ) that R ( 2 ; T ( u ) ) is an ...
Contents
Preliminary Concepts | 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 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ