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...
Cauchy integral formulas for complex functions
Cauchy operator on Bergman space of harmonic functions on unit disk
Cauchy transforms of self-similar measures.
Characteristic functional equations of polynomials and the Morera-Carleman theorem.
Computation of Poisson type integrals.
Computing Elliptic Integrals by Duplication.
Continuity on the Boundary and Analytic Continuation of Continued Fractions.
Continuous dependence of holomorphic functions on partly given boundary values
Convergence of Product Formulas for the Numerical Evaluation of Certain Two-Dimensional Cauchy Principal Value Integrals.
Correction to the paper “Continuous dependence of holomorphic functions on partly given boundary values”