Estimates for Jacobi-Sobolev type orthogonal polynomials
Abstract
Let the Sobolev-type inner product <f,g> = ∫ fg d mu0+ int f' g' d mu1 with mu0 = w + M deltac, mu1= N deltac where w is the Jacobi weight, c is either 1 or -1 and M, N >= 0. We obtain estimates and asymptotic properties on [-1,1] for the polynomials orthonormal with respect to <.,.> and their kernels. We also compare these polynomials with Jacobi orthonormal polynomials.
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