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Étude et convergence de fonctions ”spline” complexes. (Investigation and convergence of complex ”spline” functions). (French) Zbl 0592.41012
Summary: We prove the existence and the uniqueness of a complex interpolating spline function of order m, on a simply connected, bounded open subset \(\Omega\) in \({\mathbb{C}}\). Using the Aronszajn-Bergman kernels, we characterize these functions and study their convergence properties to some analytic functions on \(\Omega\). Finally, we give an application of these results to the harmonic real functions on \(\Omega\).
MSC:
41A15 Spline approximation
41A05 Interpolation in approximation theory
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