Optimal recovery of analytic functions from boundary conditions specified with error

2016 ◽  
Vol 99 (1-2) ◽  
pp. 177-182 ◽  
Author(s):  
R. R. Akopyan
Keyword(s):  
Boundary Conditions ◽  
Analytic Functions ◽  
Optimal Recovery

scholarly journals Non-Self-Adjoint Singular Sturm-Liouville Problems with Boundary Conditions Dependent on the Eigenparameter

2010 ◽  
Vol 2010 ◽  
pp. 1-10
Author(s):  
Elgiz Bairamov ◽  
M. Seyyit Seyyidoglu
Keyword(s):  
Boundary Conditions ◽  
Finite Number ◽  
Analytic Functions ◽  
Liouville Problem ◽  
Uniqueness Theorems ◽  
Spectral Singularities ◽  
Sturm Liouville ◽  
Complex Valued

Let denote the operator generated in by the Sturm-Liouville problem: , , , where is a complex valued function and , with In this paper, using the uniqueness theorems of analytic functions, we investigate the eigenvalues and the spectral singularities of . In particular, we obtain the conditions on under which the operator has a finite number of the eigenvalues and the spectral singularities.

scholarly journals A note on the characterisation of eigencurves for certain two parameter eigenvalue problems in ordinary differential equations

1993 ◽  
Vol 35 (1) ◽  
pp. 63-67 ◽  
Author(s):  
Patrick J. Browne ◽  
B. D. Sleeman
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Weight Function ◽  
Analytic Functions ◽  
Dirichlet Boundary ◽  
Eigenvalue Problems ◽  
Dirichlet Boundary Conditions ◽  
Survey Paper ◽  
Image Position ◽  
Two Parameter

We are interested in two parameter eigenvalue problems of the formsubject to Dirichlet boundary conditionsThe weight function 5 and the potential q will both be assumed to lie in L2[0,1]. The problem (1.1), (1.2) generates eigencurvesin the sense that for any fixed λ, ν(λ) is the nth eigenvalue ν, (according to oscillation indexing) of (1.1), (1.2). These curves are in fact analytic functions of λ and have been the object of considerable study in recent years. The survey paper [1] provides background in this area and itemises properties of eigencurves.

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.

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