Linear Operators: General theory |
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Page 225
... suppose that B consists of a finite collection of disjoint closed rectifiable Jordan curves ; that is , we suppose that B can be decomposed into the union B BUBU ... ○ B of dis- joint closed sets B , in such a way that each B , is a ...
... suppose that B consists of a finite collection of disjoint closed rectifiable Jordan curves ; that is , we suppose that B can be decomposed into the union B BUBU ... ○ B of dis- joint closed sets B , in such a way that each B , is a ...
Page 360
... Suppose ( i ) , ( ii ) of the last exercise . Show that if f is in BV then ( Sf ) ( x ) → f ( x ) at each point a where f is continuous . 25 Suppose that ( S „ f ) ( x ) → ( 1/2 ) ( f ( x + ) + f ( x− ) ) for each step function f ...
... Suppose ( i ) , ( ii ) of the last exercise . Show that if f is in BV then ( Sf ) ( x ) → f ( x ) at each point a where f is continuous . 25 Suppose that ( S „ f ) ( x ) → ( 1/2 ) ( f ( x + ) + f ( x− ) ) for each step function f ...
Page 570
... suppose that UUB is contained in the domain of analyticity of g . Let V be a neighborhood of o ( T ) whose boundary C consists of a finite number of rectifiable Jordan arcs , and suppose that VUC is contained in the domain of ...
... suppose that UUB is contained in the domain of analyticity of g . Let V be a neighborhood of o ( T ) whose boundary C consists of a finite number of rectifiable Jordan arcs , and suppose that VUC is contained in the domain of ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
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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