Radial Limits and growths of fractional Cauchy transforms
Random walks in with non-zero drift absorbed at the axes
Spatially homogeneous random walks in with non-zero jump probabilities at distance at most , with non-zero drift in the interior of the quadrant and absorbed when reaching the axes are studied. Absorption probabilities generating functions are obtained and the asymptotic of absorption probabilities along the axes is made explicit. The asymptotic of the Green functions is computed along all different infinite paths of states, in particular along those approaching the axes.
Randwertaufgabe von Hilbert-Typus fur die p-analytischen Funktionen und die Methode der Fourier-Schen Transformation
Rational approximation near zero sets of functions.
The paper deals with the relation between global rational approximation and local approximation off the zero set. Also connections with the problem f2 ∈ R(X) ⇒ f ∈ R(X) are studied.
Rational Chebyshev Approximation on the Unit Disk.
Rational interpolants with preassigned poles, theoretical aspects
Let ⨍ be an analytic function on a compact subset K of the complex plane ℂ, and let denote the rational function of degree n with poles at the points and interpolating ⨍ at the points . We investigate how these points should be chosen to guarantee the convergence of to ⨍ as n → ∞ for all functions ⨍ analytic on K. When K has no “holes” (see [8] and [3]), it is possible to choose the poles without limit points on K. In this paper we study the case of general compact sets K, when such a separation...
Rational interpolation: analytical solution.
Rational modules and higher order Cauchy transforms.
Ray sequences of Laurent-type rational functions.
Rectifiability, analytic capacity, and singular integrals.
Reflected double layer potentials and Cauchy's operators
Necessary and sufficient conditions are given for the reflected Cauchy's operator (the reflected double layer potential operator) to be continuous as an operator from the space of all continuous functions on the boundary of the investigated domain to the space of all holomorphic functions on this domain (to the space of all harmonic functions on this domain) equipped with the topology of locally uniform convergence.
Reflection and a mixed boundary value problem concerning analytic functions
A mixed boundary value problem on a doubly connected domain in the complex plane is investigated. The solution is given in an integral form using reflection mapping. The reflection mapping makes it possible to reduce the problem to an integral equation considered only on a part of the boundary of the domain.
Regularity of free boundaries in two dimensions
Regularization of a discrete backward problem using coefficients of truncated Lagrange polynomials.
Regularization of one class of difference equations.
Relations between the boundary values and periods for generalized analytic functions in
Remarks of the lemma of Nersesyan in complex approximation
Remarques sur les développements asymptotiques
Removable sets for Lipschitz harmonic functions in the plane.
The main motivation for this work comes from the century-old Painlevé problem: try to characterize geometrically removable sets for bounded analytic functions in C.
Représentation des fonctions par des séries de polynômes