Inverse boundary-value problems of cauchy type for harmonic functions

We apply two methods for solving the inverse boundary-value problem (the so-called problem (A)) in the Cauchy statement for an analytic function and an unknown curve ??. We obtain criteria for ?? to be the unit circle. We apply the proposed methods for solving a modified Hadamard example and generalize the obtained results for the case of doubly connected domains.     

Summability of Lagrange type interpolation series

We consider certain aspects of the theory of interpolation via entire functions of exponential type, which include sampling node sequences χ which can be highly irregular and data sequences {y(_x)}_xn∈χ which are not necessarily bounded. Under appropriate conditions, we show that there is an entire function of a suitable exponential type which uniquely interpolates the data and indicate the validity of certain summabilty methods for the corresponding Lagrange type interpolation series. Some of our results significantly extend the work of Schoenberg,Cardinal interpolation and spline functions VII: The behavior of cardinal spline interpolation as their degree tends to infinity, J. Analyse Math.27 (1974), 205–229.     

Summability of multiple Fourier series of functions of bounded generalized variation

The paper is devoted to summability problems for multiple Fourier series of functions of bounded generalized variation. We find necessary and sufficient conditions on a sequence Λ = {λ _n } that guarantee the convergence of the Cesàro means of multiple Fourier series of functions of bounded Λ-variation.     

Elliptic boundary-value problems in domains of the exterior-of-a-cusp type

One investigates general elliptic boundary-value problems in a domain DRⁿ with isolated singularities of the boundary. A common property of the considered singular points is the fact that in their neighborhoods the complement to the domain is thin. For the singular pointO this means that the central projection of the set onto the sphere shrinks to a point as One proves theorems on the normal solvability in Sobolev spaces with weighted norms, one obtains coercive estimates of the solutions, one investigates the properties of the solutions in dependence on the properties of the right-hand sides.Translated from Problemy Matematicheskogo Analiza, No. 9, pp. 105–148, 1984.     

Spline functions as approximate solutions of boundary-value problems

In this paper, an algorithm for finding a spline function that will satisfy a given linear differential equation at a discrete set of points and a given set of boundary conditions is described.     

On the method of complementary functions for nonlinear boundary-value problems

We show that, like the method of adjoints, the method of complementary functions can be effectively used to solve nonlinear boundary-value problems.This work was supported by the Alexander von Humboldt Foundation. The author is thankful to Prof. G. Hämmerlin for providing the facilities and to Miss J. Gumberger for performing numerical tests. The author is also indebted to Dr. S. M. Roberts for his suggestions on the first draft of this paper.     

On the solution of boundary-value problems of Kolmogorov-Petrovskii-Piskunov type

We describe a number of properties of solutions of boundary-value problems for nonlinear ordinary differential equations of the same type as those studied by Kolmogorov, Petrovskii, and Piskunov in their well-known paper on waves described by the parabolic equation. We construct and justify the asymptotics of such solutions for large values of the modulus of the independent variable.     

Summability of Fourier series for almost-periodic functions on locally compact Abelian groups

Some results concerning the summability of Fourier series of continuous 2π-periodic functions are generalized for the case of almost-periodic functions defined on locally compact Abelian groups.     

Solution of nonlinear two-point boundary-value problems using spline functions

Journal of Optimization Theory and Applications - This paper describes a technique for computing spline function approximations to the solution of two-point boundary-value problems. A performance...     

Second order initial boundary-value problems of variational type

We consider linear hyperbolic boundary-value problems for second order systems, which can be written in the variational form δL=0, with

     

Summability of orthogonal series with speed

Summary Some sufficient conditions are found for summability of orthogonal series with speed.     

Solving boundary-value problems ofx k -analytic functions for a semicircle

Integral representations of x^k-analytic functions (k=const>0) in terms of boundary values of analytic functions are given. Using these integral representations, three boundary-value problems of x^k-analytic functions for a semicircle are solved by quadratures. Bibliography: 4 titles. Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 76, 1992, pp. 3–12.