On orthogonal polynomials for certain nondefinite linear functionals

On orthogonal polynomials for certain nonde nite linear functionals

We consider the non-de nite linear functionals Ln[f] = ∫ R w(x)f (x) dx and prove the nonexistence of orthogonal polynomials, with all zeros real, in several cases. The proofs are based on the connection with moment preserving spline approximation. c © 1998 Elsevier Science B.V. All rights reserved.

On orthogonal polynomials for certain non-definite linear functionals

We consider the non-definite linear functionals Ln[f ] = ∫ IR w(x)f (n)(x) dx and prove the nonexistence of orthogonal polynomials, with all zeros real, in several cases. The proofs are based on the connection with moment preserving spline approximation.

Orthogonal polynomials for refinable linear functionals

A refinable linear functional is one that can be expressed as a convex combination and defined by a finite number of mask coefficients of certain stretched and shifted replicas of itself. The notion generalizes an integral weighted by a refinable function. The key to calculating a Gaussian quadrature formula for such a functional is to find the three-term recursion coefficients for the polynomi...

Note on Certain Orthogonal Polynomials

On Certain Wronskians of Multiple Orthogonal Polynomials

We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multi-indices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians keep a constant sign in some cases, while in some other cases oscillatory behavior appears, which generalizes cla...