A remark on Hartogs' double series
A remark on uniqueness of best rational approximants of degree 1 in of the circle.
A Riemann–Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves
A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators
We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.
A set of tangential approximation by meromorphic functions.
A Sinc Quadrature Rule for Hadamard Finite-part Integrals.
A singular controllability problem with vanishing viscosity
The aim of this paper is to answer the question: Do the controls of a vanishing viscosity approximation of the one dimensional linear wave equation converge to a control of the conservative limit equation? The characteristic of our viscous term is that it contains the fractional power α of the Dirichlet Laplace operator. Through the parameter α we may increase or decrease the strength of the high frequencies damping which allows us to cover a large class of dissipative mechanisms. The viscous term,...
A summability approximation theorem for Taylor series of meromorphic functions.
A survey on geometric properties of holomorphic self-maps in some domains of ℂⁿ
In this survey we give geometric interpretations of some standard results on boundary behaviour of holomorphic self-maps in the unit disc of ℂ and generalize them to holomorphic self-maps of some particular domains of ℂⁿ.
A system of exponential functions with shift and the Kostyuchenko problem.
A topological dichotomy with applications to complex analysis
Let X be a compact topological space, and let D be a subset of X. Let Y be a Hausdorff topological space. Let f be a continuous map of the closure of D to Y such that f(D) is open. Let E be any connected subset of the complement (to Y) of the image f(∂D) of the boundary ∂D of D. Then f(D) either contains E or is contained in the complement of E. Applications of this dichotomy principle are given, in particular for holomorphic maps, including maximum and minimum modulus principles,...
A weak type inequality for Cauchy transforms of finite measures.
In this note we present a simple proof of a recent result of Mattila and Melnikov on the existence of limε→0 ∫|ζ-z|>ε (ζ - z)-1dμ(ζ) for finite Borel measures μ in the plane.
A weighted interpolation problem for analytic functions
About the derivatives of Cauchy type integrals in the polydisc.
Absolutely continuous measures and compact composition operator on spaces of Cauchy transforms.
Absolutely continuous measures and compact composition operator on spaces of Cauchy transforms.
Accelero-summation of the formal solutions of nonlinear difference equations
In 1996, Braaksma and Faber established the multi-summability, on suitable multi-intervals, of formal power series solutions of locally analytic, nonlinear difference equations, in the absence of “level ”. Combining their approach, which is based on the study of corresponding convolution equations, with recent results on the existence of flat (quasi-function) solutions in a particular type of domains, we prove that, under very general conditions, the formal solution is accelero-summable. Its sum...
Aleksandrov-Clark measures and semigroups of analytic functions in the unit disc.
Algebras of Toeplitz operators with oscillating symbols.
This paper is devoted to Banach algebras generated by Toeplitz operators with strongly oscillating symbols, that is, with symbols of the form b[eia(x)] where b belongs to some algebra of functions on the unit circle and a is a fixed orientation-preserving homeomorphism of the real line onto itself. We prove the existence of certain interesting homomorphisms and establish conditions for the normal solvability, Fredholmness, and invertibility of operators in these algebras.
Algorithms for Evaluation of the Wright Function for the Real Arguments’ Values
2000 Math. Subject Classification: 33E12, 65D20, 33F05, 30E15The paper deals with analysis of several techniques and methods for the numerical evaluation of the Wright function. Even if the focus is mainly on the real arguments’ values, the methods introduced here can be used in the complex plane, too. The approaches presented in the paper include integral representations of the Wright function, its asymptotic expansions and summation of series. Because the Wright function depends on two parameters ...