Calculating Singular Integrals as an Ill-posed Problem.
Calderón's problem for Lipschitz classes and the dimension of quasicircles.
In the last years the mapping properties of the Cauchy integralCΓf(z) = 1/(2πi) ∫Γ [f(ξ) / ξ - z] dξhave been widely studied. The most important question in this area was Calderón's problem, to determine those rectifiable Jordan curves Γ for which CΓ defines a bounded operator on L2(Γ). The question was solved by Guy David [Da] who proved that CΓ is bounded on L2(Γ) (or on Lp(Γ), 1 < p < ∞) if and only if Γ is regular, i.e.,H1(Γ ∩ B(z0,R) ≤ CRfor every z0 ∈ C, R > 0 and for...
Carlemann Approximation on Riemann Surfaces.
Cauchy integral formulas for complex functions
Cauchy operator on Bergman space of harmonic functions on unit disk
Cauchy transforms of self-similar measures.
Causality and local analyticity : mathematical study
Characteristic functional equations of polynomials and the Morera-Carleman theorem.
Characterization of linear functionals associated with bilinear forms of Sobolev type.
Chebyshev approximation via polynomial mappings and the convergence behaviour of Krylov subspace methods.
Coincidence of some classes of universal functions.
Complete interpolating sequences for Paley-Wiener spaces and Muckenhoupt's (Ap) condition.
We describe the complete interpolating sequences for the Paley-Wiener spaces Lπp (1 < p < ∞) in terms of Muckenhoupt's (Ap) condition. For p = 2, this description coincides with those given by Pavlov [9], Nikol'skii [8] and Minkin [7] of the unconditional bases of complex exponentials in L2(-π,π). While the techniques of these authors are linked to the Hilbert space geometry of Lπ2, our method of proof is based in turning the problem into one about boundedness of the Hilbert transform...
Computation of Poisson type integrals.
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