For a wide class of weights, a systematic investigation of the convergence-divergence behavior of Lagrange interpolation is initiated. A system of nodes with optimal Lebesgue constant is found, and for Hermite weights an exact lower estimate of the norm of projection operators is given. In the same spirit, the case of Hermite-Fej6r interpolation is also considered.

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We study solutions pxnq nPN of nonhomogeneous nonlinear second available online: MMM DD, 2014. 2010 Mathematics Subject Classification. 39A22, 65Q10, 65Q30. Key words and phrases. nonhomogeneous nonlinear second order difference equations, Shohat-Freud-type exponential weight functions, Painlevé's discrete equation #1, existence of solutions, unicity of solutions, asymptotic behavior.

In this paper we give sharp Markov Bernstein type inequalities for derivatives of multivariate polynomials for a wide family of domains with cusps. AcademicPress