Quasi-orthogonality of some hypergeometric polynomials

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 extend previous results on the quasi-orthogonality of Jacobi polynomials and discuss the quasi-orthogonality of Meixner–Pollaczek, Hahn, Dual-Hahn and Continuous Dual-Hahn polynomials using a characterization of quasi-orthogonality due to Shohat. Of particular interest are the Meixner–Pollaczek polynomials whose linear combinations only exhibit quasi-orthogonality of even order. In some cases, we also investigate the location of the zeros of these polynomials for quasi-orthogonality of order 1 and 2 with respect to the end points of the interval of orthogonality, as well as with respect to the zeros of different polynomials in the same orthogonal sequence.     

A note on the Conley attractors of lower semicontinuous multifunctions

We discuss Conley-type approach to attractive sets for lower semicontinuous multifunctions. Since every iterated function system induces a Barnsley–Hutchinson multifunction which is l.s.c. in such a case it is much more natural to consider a multifunctions of that type then closed relations on compact spaces earlier considered by some authors. We use topological (Kuratowski’s) limit instead of commonly used Hausdorff metric.     

The lower bound of the number of nonabelian subgroups of finite p-groups

In this paper, we give the lower bound of the number of nonabelian subgroups of possible index of finite p-groups, and classify the finite p-groups such that the number of nonabelian subgroups of possible order are exactly the lower bound.