Computing Elliptic Integrals by Duplication.
Conformal mapping of the domain bounded by a circular polygon with zero angles onto the unit disc
The conformal mapping ω(z) of a domain D onto the unit disc must satisfy the condition |ω(t)| = 1 on ∂D, the boundary of D. The last condition can be considered as a Dirichlet problem for the domain D. In the present paper this problem is reduced to a system of functional equations when ∂D is a circular polygon with zero angles. The mapping is given in terms of a Poincaré series.
Continued Fractions Associated With the Newton-Padé Table.
Continuity and convergence properties of extremal interpolating disks.
Let a be a sequence of points in the unit ball of Cn. Eric Amar and the author have introduced the nonnegative quantity ρ(a) = infα infk Πj:j≠k dG(αj, αk), where dG is the Gleason distance in the unit disk and the first infimum is taken over all sequences α in the unit disk which map to a by a map from the disk to the ball.The value of ρ(a) is related to whether a is an interpolating sequence with respect to analytic disks passing through it, and if a is an interpolating sequence in the ball, then...
Continuity on the Boundary and Analytic Continuation of Continued Fractions.
Continuity properties of best analytic approximation.
Continuous dependence of holomorphic functions on partly given boundary values
Continuous symmetrized Sobolev inner products of order . II.
Convergence of Padé approximants for a q-hypergeometric series (Wynn's Power Series III).
Convergence of Padé approximants for a q-hypergeometric series (Wynn's Power Series III). (Summary).
Convergence of Padé approximants for a q-hypergeometric series (Wynn's Power Series I). (Summary).
Convergence of Padé approximations for a q-hypergeometric series (Wynn's Power Series I).
Convergence of Product Formulas for the Numerical Evaluation of Certain Two-Dimensional Cauchy Principal Value Integrals.
Convergence of rational interpolants.
Correction to the paper “Continuous dependence of holomorphic functions on partly given boundary values”
Croissance et meilleure approximation polynomiale des fonctions entieres
Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space
2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.In this paper we consider an L^2 type space of scalar functions L^2 M, A (R u iR) which can be, in particular, the usual L^2 space of scalar functions on R u iR. We find conditions for density of polynomials in this space using a connection with the L^2 space of square-integrable matrix-valued functions on R with respect to a non-negative Hermitian matrix measure. The completness of L^2 M, A (R u iR ) is also established.
Density theorems for sampling and interpolation in the Bargmann-Fock space III.
Der Zusammenhang zwischen der Randwertaufgabe von Riemann und einem Problem der mathematischen Musiktheorie
Derivative and antiderivative operators and the size of complex domains
We prove some conditions on a complex sequence for the existence of universal functions with respect to sequences of certain derivative and antiderivative operators related to it. These operators are defined on the space of holomorphic functions in a complex domain. Conditions for the equicontinuity of those sequences are also studied. The conditions depend upon the size of the domain.