An analogue of the two-constants theorem and optimal recovery of analytic functions

2019 ◽  
Vol 210 (10) ◽  
pp. 1348-1360
Author(s):  
R. R. Akopyan
Keyword(s):  
Analytic Functions ◽  
Optimal Recovery

scholarly journals About the Optimal Recovery of Derivatives of Analytic Functions from Their Values at Points That Form a Regular Polygon

2019 ◽  
pp. 30-38
Author(s):  
Mikhail Ovchintsev
Keyword(s):  
Approximation Method ◽  
Blaschke Product ◽  
Analytic Functions ◽  
Best Approximation ◽  
Extremal Function ◽  
Regular Polygon ◽  
Optimal Recovery ◽  
Bounded Analytic Functions ◽  
The Best Approximation ◽  
Derivatives Of

In this paper, the author solves the problem of optimal recovery of derivatives of bounded analytic functions defined at the zero of the unit circle. Recovery is performed based on information about the values of these functions at points z1, ... , zn , that form a regular polygon. The article consists of an introduction and two sections. The introduction talks about the necessary concepts and results from the works of Osipenko K.Yu. and Khavinson S.Ya., that form the basis for the solution of the problem. In the first section, the author proves some properties of the Blaschke product with zeros at the points z1, ... , zn. After this, the error of the best approximation method of the derivatives f(N)(0), 1 ≤ N ≤ n − 1, by the values f(z1), ... , f(zn) is calculated. In the same section he gives the corresponding extremal function. In the second section, the uniqueness of the linear best approximation method is established, and then its coefficients are calculated. At the end of the article, the formulas found for calculating of the coefficients are substantially simplified.

Optimal Recovery of the Derivative of Bounded Analytic Functions

1983 ◽  
Vol 3 (3) ◽  
pp. 327-332 ◽  
Author(s):  
T. J. RIVLIN ◽  
ST. RUSCHEWEYH ◽  
D. SHAFFER ◽  
K. J. WIRTHS
Keyword(s):  
Analytic Functions ◽  
Optimal Recovery ◽  
Bounded Analytic Functions

Studies on the Fibrinolytic System in Human Plasma: Quantitative Determination of Plasminogen Activators and Proactivators

1979 ◽  
Vol 41 (02) ◽  
pp. 365-383 ◽  
Author(s):  
C Kluft
Keyword(s):  
Pilot Study ◽  
Plasma Level ◽  
Human Plasma ◽  
Plasminogen Activators ◽  
Venous Occlusion ◽  
Quantitative Information ◽  
Optimal Recovery ◽  
Dextran Sulphate ◽  
Baseline Levels

SummaryEffects due to plasma plasminogen activators and proactivators are usually studied in assay systems where inhibitors influence the activity and where the degree of activation of proactivators is unknown. Quantitative information on activator and proactivator levels in plasma is therefore not availableStudies on the precipitating and activating properties of dextran sulphate in euglobulin fractionation presented in this paper resulted in the preparation of a fraction in which there was optimal recovery and optimal activation of a number of plasminogen activators and proactivators from human plasma. The quantitative assay of these activators on plasminogen-rich fibrin plates required the addition of flufenamate to eliminate inhibitors. The response on the fibrin plates (lysed zones) could be coverted to arbitrary blood activator units (BAU). Consequently, a new activator assay which enables one to quantitatively determine the plasma level of plasminogen activators and proactivators together is introduced.Two different contributions could be distinguished: an activity originating from extrinsic activator and one originating from intrinsic proactivators. The former could be assayed separately by means of its resistance to inhibition by Cl-inactivator. Considering the relative concentrations of extrinsic and intrinsic activators, an impression of the pattern of activator content in plasma was gained. In morning plasma with baseline levels of fibrinolysis, the amount of extrinsic activator was negligible as compared to the level of potentially active intrinsic activators. Consequently, the new assay nearly exclusively determines the level of intrinsic activators in morning plasma. A pilot study gave a fairly stable level of 100 ± 15 BAU/ml (n = 50). When fibrinolysis was stimulated by venous occlusion (15 min), the amount of extrinsic activator was greatly increased, reaching a total activator level of 249 ± 27 BAU/ml (n = 7).

Sign in / Sign up

Export Citation Format

Share Document