On an integral operator in the space of functions with bounded variation. II.
On Bateman's Method for Second Kind Integral Equations.
On empirical stochastic regularization
On Fredholm integral equations with random degenerate kernels
On Fredholm-Stieltjes integral equations (Preliminary communication)
On one Fredholm integral equation of third kind.
On solutions of integral equations with analytic kernels and rotations
We deal with a class of integral equations on the unit circle in the complex plane with a regular part and with rotations of the form (*) x(t) + a(t)(Tx)(t) = b(t), where and are of the form (3) below. We prove that under some assumptions on analytic continuation of the given functions, (*) is a singular integral equation for m odd and is a Fredholm equation for m even. Further, we prove that T is an algebraic operator with characteristic polynomial . By means of the Riemann boundary value...
On solvability of boundary value problem for elliptic equations with Bitsadze-Samarskij condition.
On the boundness of the Stokes semigroup in two-dimensional exterior domains.
On the efficient use of the Galerkin-method to solve Fredholm integral equations
In the present paper we describe, how to use the Galerkin-method efficiently in solving boundary integral equations. In the first part we show how the elements of the system matrix can be computed in a reasonable time by using suitable coordinate transformations. These techniques can be applied to a wide class of integral equations (including hypersingular kernels) on piecewise smooth surfaces in 3-D, approximated by spline functions of arbitrary degree. In the second part we show, how to use the...
On the existence and uniqueness of integrable solutions of functional equations in Banach space.
On the existence of exactly one solution of integral equations in the space with a mixed norm
On the Karhunen-Loeve expansion for transformed processes.
We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f-2(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.
On the low wave number behavior of two-dimensional scattering problems for an open arc.
On the Regularization of Projection Methods for Solving Ill-Posed Problems.
On the Spectra of Finite-Dimensional Pertobations of Matrix Multiplication Operators.
On the stability of Runge-Kutta methods for delay integral equations.