Linear Operators: General theory |
From inside the book
Results 1-3 of 63
Page 140
... intervals . An interval is finite if both its end points are finite ; otherwise it is an infinite interval . If ƒ is a complex function on an interval I , the total variation of f on I is defined by the equation n --- v ( f , I ) = sup ...
... intervals . An interval is finite if both its end points are finite ; otherwise it is an infinite interval . If ƒ is a complex function on an interval I , the total variation of f on I is defined by the equation n --- v ( f , I ) = sup ...
Page 141
... interval I = ( a , b ) which may be finite or infinite . It is assumed that ( i ) f ( s ) = lim f ( s + e ) , 0 < -3 € sel ; = i.e. , f is continuous on the right at every point in the open interval I. The closed interval Ī [ a , b ] is ...
... interval I = ( a , b ) which may be finite or infinite . It is assumed that ( i ) f ( s ) = lim f ( s + e ) , 0 < -3 € sel ; = i.e. , f is continuous on the right at every point in the open interval I. The closed interval Ī [ a , b ] is ...
Page 223
... interval ( a , b ) and continuous on the right . Let g be a function defined on ( a , b ) such that the Lebesgue - Stieltjes integral I = Sag ( s ) dh ( s ) exists . Let ƒ be a continuous increasing function on an open interval ( c , d ) ...
... interval ( a , b ) and continuous on the right . Let g be a function defined on ( a , b ) such that the Lebesgue - Stieltjes integral I = Sag ( s ) dh ( s ) exists . Let ƒ be a continuous increasing function on an open interval ( c , d ) ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
40 other sections not shown
Other editions - View all
Common terms and phrases
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