ON A CLASS OF POLYNOMIALS ORTHOGONAL WITH RESPECT TO A DISCRETE SOBOLEV INNER PRODUCT

This paper analyzes polynomials orthogonal with respect to the Sobolev inner product phi-approximately(f,g) = Integral f(x)g(x)Q(x)dx+lambda-1f(r)(c)?? g((r))(C) with lambda epsilon R+, c epsilon R, and Q(x) is a weight function. We study this family of orthogonal polynomials, as linked to the polynomials orthogonal with respect to Q(x) and we find the recurrence relation verified by such a family. If the weight Q is semiclassical we obtain a second order differential equation for these polynomials. Finally, an illustrative example is shown.