Orthogonality with respect to a Jacobi differential operator and applications

Abstract

Let μ be a finite positive Borel measure on [−1,1], m a fixed natural number and L(α,β)[f]=(1−x2)f″+(β−α−(α+β+2)x)f′, with α,β>−1. We study algebraic and analytic properties of the sequence of monic polynomials (Qn)n>m that satisfy the orthogonality relations ∫L(α,β)[Qn](x)xkdμ(x)=0for all 0≤k≤n−1. A fluid dynamics model for source points location of a flow of an incompressible fluid with preassigned stagnation points is also considered.