P. Turán [!Tu] proved that if all the zeros of a polyniomial p lie in the unit interval I def = [−1, 1], then ‖p‖L∞(I) ≥ √ deg(p)/6 ‖p‖L∞(I) . Our goal is to study the feasibility of limn→∞ ‖pn‖X/‖pn‖Y = ∞ for sequences of polynomials {pn}n∈N whose zeros satisfy certain conditions, and to obtain lower bounds for derivatives of (generalized) polynomials and Remez type inequalities for generalize...

We report about results revolving around Kostka–Foulkes and parabolic Kostka polynomials and their connections with Representation Theory and Combinatorics. It appears that the set of all parabolic Kostka polynomials forms a semigroup, which we call Liskova semigroup. We show that polynomials frequently appearing in Representation Theory and Combinatorics belong to the Liskova semigroup. Among ...

We introduce the sequence of generalized Gončarov polynomials, which is a basis for the solutions to the Gončarov interpolation problem with respect to a delta operator. Explicitly, a generalized Gončarov basis is a sequence (tn(x))n≥0 of polynomials defined by the biorthogonality relation εzi(d (tn(x))) = n!δi,n for all i, n ∈ N, where d is a delta operator, Z = (zi)i≥0 a sequence of scalars, ...

Abstract. In [18], the new q-extension of Bernoulli polynomials and generalized Bernoulli numbers attached to χ were constructed by using p-adic invariant integral on Zp. In this paper we construct the new q-extension of generalized Bernoulli polynomials attached to χ due to author and derive the existence of a specific p-adic interpolation function which interpolate the q-extension of generali...