On a problem of linear conjugation in the case of nonsmooth lines and some measurable coefficients.
On a representation of the derivative of a conformal mapping.
On a residue of complex functions in the three-dimensional Euclidean complex vector space.
On applicability of the projection method to two-dimensional Toeplitz operators with measurable symbol.
On boundary behavior of Cauchy integrals
In this paper, we shall estimate the growth order of the n-th derivative Cauchy integrals at a point in terms of the distance between the point and the boundary of the domain. By using the estimate, we shall generalize Plemelj-Sokthoski theorem. We also consider the boundary behavior of generalized Cauchy integrals on compact bordered Riemann surfaces.
On defining the generalized functions and .
On families of Cauchy transformations.
On numerical cubatures of singular surface integrals in boundary element methods.
On Phragmén-Lindelöf principle of type .
On the analytic capacity and curvature of some Cantor sets with non-σ-finite length.
We show that if a Cantor set E as considered by Garnett in [G2] has positive Hausdorff h-measure for a non-decreasing function h satisfying ∫01 r−3 h(r)2 dr < ∞, then the analytic capacity of E is positive. Our tool will be the Menger three-point curvature and Melnikov’s identity relating it to the Cauchy kernel. We shall also prove some related more general results.
On the Convergence of a Quadrature Rule for Evaluating Certain Cauchy Principal Value Integrals: An Addendum.
On the Derivative of Some Analytic Functions.
On the Existence of Principal Values for the Cauchy Integral on Weighted Lebesgue Spaces for Non-Doubling Measures.
On the Integrability of the Derivative of a Quasiregular Mapping.
On the logarithmic potential defined for a Van Koch curve.
On the Neumann-Poincaré operator
Let be a rectifiable Jordan curve in the finite complex plane which is regular in the sense of Ahlfors and David. Denote by the space of all complex-valued functions on which are square integrable w.r. to the arc-length on . Let stand for the space of all real-valued functions in and put Since the Cauchy singular operator is bounded on , the Neumann-Poincaré operator sending each into is bounded on . We show that the inclusion characterizes the circle in the class of all...
On the numerical solution of the multidimensional singular integrals and integral equations, used in the theory of linear viscoelasticity.
On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals.
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