Lebesgue Sobolev orthogonality on the unit circle

Hermite Interpolation and Sobolev Orthogonality

Sobolev orthogonality has been studied for years. For different families of polynomials, there exist several results about recurrence relations, asymptotics, algebraic and differentation properties, zeros, etc. (see, for instance, Alfaro et al. (1999), Jung et al. (1997), Kwon and Littlejohn (1995, 1998), Marcellán et al. (1996), Pérez and Piñar (1996)); but there exist very few results establi...

On computational aspects of discrete Sobolev inner products on the unit circle

On the Unit Circle

New characterizations are given for orthogonal polynomials on the unit circle and the associated measures in terms of the reflection coefficients in the recurrence equation satisfied by the polynomials.

Generalized Coherent Pairs on the Unit Circle and Sobolev Orthogonal Polynomials

A pair of regular Hermitian linear functionals (U ,V) is said to be an (M,N)-coherent pair of order m on the unit circle if their corresponding sequences of monic orthogonal polynomials {φn(z)}n>0 and {ψn(z)}n>0 satisfy M ∑ i=0 ai,nφ (m) n+m−i(z) = N ∑ j=0 bj,nψn−j(z), n > 0, where M,N,m > 0, ai,n and bj,n, for 0 6 i 6 M , 0 6 j 6 N , n > 0, are complex numbers such that aM,n 6= 0, n > M , bN,n...

The best n-dimensional linear approximation of the Hardy operator and the Sobolev Classes on unit circle and on line

Let I = [a, b] with −∞ < a < b < ∞ and 1 < p < ∞. Let