Linear Operators: General theory |
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Page 3
... domain of ƒ contains the domain of g , and f ( x ) = g ( x ) for x 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 x 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 538
... domain a < ≈ < b and having values in a B - space X. Show that if M ( r ) = max | f ( z ) | , log M ( r ) is a convex function of log r , a < r < b . | z | = r 49 ( Hardy ) Let ƒ be a complex - valued analytic function defined in the ...
... domain a < ≈ < b and having values in a B - space X. Show that if M ( r ) = max | f ( z ) | , log M ( r ) is a convex function of log r , a < r < b . | z | = r 49 ( Hardy ) Let ƒ be a complex - valued analytic function defined in the ...
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