Estimates for jacobi—sobolev type orthogonal polynomials

Abstract

Abstract. Let the Sobolev-type inner productwith µ 0 = w + M δ c , µ 1 = N δ c 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.

A Cohen-Type Inequality for Jacobi-Sobolev Expansions

“…f (x)g(x)dμ(x) + M f (1)g (1) + N f (1)g (1), (1.3) where M ≥ 0, N ≥ 0. We denote by {q (α,β) n } n≥0 the sequence of orthonormal polynomials with respect to the inner product (1.3) (see [1,2]).…”

“…We denote by {q (α,β) n } n≥0 the sequence of orthonormal polynomials with respect to the inner product (1.3) (see [1,2]). These polynomials are known in the literature as Jacobi-Sobolev-type polynomials.…”

“…[1]). Throughout this paper, positive constants are denoted by c,c 1 ,... and they may vary at every occurrence.…”

Divergent Cesàro Means of Jacobi-Sobolev Expansions

“…Some basic properties of the polynomials q (α,β) n (see [1]) that we will need in the sequel, are given in below: …”

“…We denote by {q (α,β) n } n≥0 the sequence of orthonormal polynomials with respect to the inner product (1) (see [1]). These polynomials are known in the literature as Jacobi-Sobolev type polynomials.…”