Using Casorati determinants of Charlier polynomials (ca n )n , we construct for each finite set F of positive integers a sequence of polynomials cF n , n ∈ σF , which are eigenfunctions of a second order difference operator, where σF is certain infinite set of nonnegative integers, σF ( N. For suitable finite sets F (we call them admissible sets), we prove that the polynomials cF n , n ∈ σF , a...

We describe the limit zero distributions of sequences of polynomials with positive coefficients. We also characterize the polynomials with real coefficients for which some power has positive coefficients. MSC Primary: 30C15, 26C10, secondary: 31A05.

Using Casorati determinants of Meixner polynomials (m n )n , we construct for each pair F = (F1, F2) of finite sets of positive integers a sequence of polynomials ma,c;F n , n ∈ σF , which are eigenfunctions of a second order difference operator, where σF is certain infinite set of nonnegative integers, σF N. When c and F satisfy a suitable admissibility condition, we prove that the polynomials...

A bad point of a positive semidefinite real polynomial f is at which pole appears in all expressions as sum squares rational functions. We show that quartic polynomials three variables never have points. give examples with the origin, are nevertheless sums formal power series, answering question Brumfiel. also an example complex not real, Scheiderer.

Hilbert's 17th problem concerns expressing polynomials on R as a sum of squares. It is well known that many positive polynomials are not sums of squares; see [R00] [deA preprt] for excellent surveys. In this paper we consider symmetric non-commutative polynomials and call one \matrix positive", if whenever matrices of any size are substituted for the variables in the polynomial the matrix value...

Four recursive constructions of permutation polynomials over GF(q2) with those over GF(q) are developed and applied to a few famous classes of permutation polynomials. They produce infinitely many new permutation polynomials over GF(q2 l ) for any positive integer l with any given permutation polynomial over GF(q). A generic construction of permutation polynomials over GF(22m) with o-polynomial...