Linear Operators: General theory |
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Page 3
... domain of ƒ contains the domain of g , and f ( x ) = g ( x ) for a in the domain of g . The restriction of a function f to a subset A of its domain is sometimes denoted by f | A . If ƒ : A → B , and for each be f ( A ) there is only ...
... domain of ƒ contains the domain of g , and f ( x ) = g ( x ) for a in the domain of g . The restriction of a function f to a subset A of its domain is sometimes denoted by f | A . If ƒ : A → B , and for each be f ( A ) there is only ...
Page 230
... domain U in Z is connected if and only if every pair of its points lies on some simple Jordan curve contained in U. Let f be a function analytic on a domain U in the space of n complex variables , and let g be an analytic function ...
... domain U in Z is connected if and only if every pair of its points lies on some simple Jordan curve contained in U. Let f be a function analytic on a domain U in the space of n complex variables , and let g be an analytic function ...
Page 710
... domain μ > [ V ] and it evidently depends analytically on μ . Since | R ( μ ; V ) | → 0 as μ → ∞ , it follows that for μ sufficiently large | R ( μ ; V ) K | < 1. By Lemma VII.3.4 we conclude that if | μ is suffi- ciently large ...
... domain μ > [ V ] and it evidently depends analytically on μ . Since | R ( μ ; V ) | → 0 as μ → ∞ , it follows that for μ sufficiently large | R ( μ ; V ) K | < 1. By Lemma VII.3.4 we conclude that if | μ is suffi- ciently large ...
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