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 , 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 21 , 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 588
... analytic function by 4 ( u ) . Since , for ud2 , the function △ ( μ ) ‡ 0 , its reciprocal , and therefore each t ;, is analytic . Thus the ti , are analytic for │μ < d2 . If T1 ( u ) denotes the restriction of T ( u ) to the m ...
... analytic function by 4 ( u ) . Since , for ud2 , the function △ ( μ ) ‡ 0 , its reciprocal , and therefore each t ;, is analytic . Thus the ti , are analytic for │μ < d2 . If T1 ( u ) denotes the restriction of T ( u ) to the m ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
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A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz 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