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Irreducibility criteria for reciprocal polynomials and applications
(Mathematical Association of America, 2017-01)
We present criteria for determining irreducibility of reciprocal polynomials over the field of rational numbers. We also obtain some combinatorial results concerning the irreducibility of reciprocal polynomials. As a ...
On the measure of polynomials attaining maxima on a vertex
(Element, 2019-03)
We calculate the probability that a k-homogeneous polynomial in n variables attain a local maximum on a vertex in terms of the “sharpness” of the vertex, and then study the dependence of this measure on the growth of ...
New Classes of Degenerate Unified Polynomials
(SwitzerlandSwitzerland, 2023)
Tchakaloff’s theorem and k-integral polynomials in Banach spaces
(American Mathematical Society, 2017-08)
Tchakaloff’s theorem gives a quadrature formula for polynomials of a given degree with respect to a compactly supported positive measure which is absolutely continuous with respect to Lebesgue measure. We study the validity ...
On the convergence of random polynomials and multilinear forms
(Academic Press Inc Elsevier Science, 2011-10)
We consider different kinds of convergence of homogeneous polynomials and multilinear forms in random variables. We show that for a variety of complex random variables, the almost sure convergence of the polynomial is ...
M-structures in vector-valued polynomial spaces
(Heldermann Verlag, 2012-12)
This paper is concerned with the study of M-structures in spaces of polynomials. More precisely, we discuss for E and F Banach spaces, whether the class of weakly continuous on bounded sets n-homogeneous polynomials, Pw(nE; ...
Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)
(Springer, 2017-06)
Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of (SU (2) × SU (2) , diag) are introduced and studied in detail. The quantum symmetric pair is given in terms of a quantised ...
Factoring bivariate sparse (lacunary) polynomials
(Academic Press Inc Elsevier Science, 2007-12)
We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K [x, y] over an algebraic number field K and their multiplicities, whose running time is polynomial ...
Extending polynomials in maximal and minimal ideals
(Kyoto Univeristy, 2010-03)
Given a homogeneous polynomial on a Banach space E belonging to some maximal or minimal polynomial ideal, we consider its iterated extension to an ultrapower of E and prove that this extension remains in the ideal and has ...