ABSTRACT The sequences of quasi-orthogonal polynomials of order r are defined for non-quasi-definite moment functionals. Properties concerning the existence of such sequences, and relations between a… Expand

ABSTRACT The zeros of quasi-orthogonal polynomials play a key role in applications in areas such as interpolation theory, Gauss-type quadrature formulas, rational approximation and electrostatics. We… Expand

In this paper we study quasi-orthogonality on the unit circle based on the structural and orthogonal properties of a class of self-invariant polynomials. We discuss a special case in which these… Expand

We consider interlacing properties satisfied by the zeros of Jacobi polynomials in quasi-orthogonal sequences characterised by > 1, 2 1 and 2 1, 2 < < 1. The interlacing of zeros of P (; ) n and P (;… Expand

A result of P\'olya states that every sequence of quadrature formulas $Q_n(f)$ with $n$ nodes and positive numbers converges to the integral $I(f)$ of a continuous function $f$ provided $Q_n(f)=I(f)$… Expand

The aim of this paper are two folds. The first part is concerned with the associated and the so-called co-polynomials, i.e., new sequences obtained when finite perturbations of the recurrence… Expand

where the { pn(X) } n??= are the related orthogonal polynomials. We say that two polynomial sets are related if one set is quasi-orthogonal with respect to the interval and distribution of the… Expand