Determination of the basis of the space of all root functionals of a system of polynomial equations and of the basis of its ideal by the operation of the extension of bounded root functionals (Presented by Corresponding Member of the NAS of Ukraine A. A. Letichevsky) The notion of a root functional of a system of polynomials or an ideal of polynomials is a generalization of the notion of a root...

This article is devoted to the problem of operator interpolation and functional differentiation. Some information about variational derivatives explicit formulas for exact solutions simplest equations containing first required are given. For functionals defined on sets functions square matrices, various interpolating polynomials Hermitе type with nodes second multiplicity, which contain interpo...

The main objects of the investigation presented in this paper are branched-continued-fraction representations ratios contiguous hypergeometric series and type II multiple orthogonal polynomials on step-line with respect to linear functionals or measures whose moments products Pochhammer symbols. This is an interesting case study recently found connection between branched continued fractions tha...

Finite-dimensional representations of Onsager’s algebra are characterized by the zeros of truncation polynomials. The ZN -chiral Potts quantum chain hamiltonians (of which the Ising chain hamiltonian is the N = 2 case) are the main known interesting representations of Onsager’s algebra and the corresponding polynomials have been found by Baxter and Albertini, McCoy and Perk in 1987-89 consideri...

We present a general technique for obtaining permutation polynomials over a finite field from permutations of a subfield. By applying this technique to the simplest classes of permutation polynomials on the subfield, we obtain several new families of permutation polynomials. Some of these have the additional property that both f(x) and f(x) + x induce permutations of the field, which has combin...

Zeros of Kac polynomials spanned by monomials with i.i.d. random coefficients are asymptotically uniformly distributed near the unit circumference. We give estimates of the expected discrepancy between the zero counting measure and the normalized arclength on the unit circle. Similar results are established for polynomials with random coefficients spanned by different bases, e.g., by orthogonal...

where A and B are fixed polynomials with degA ≤ 2, and degB = 1. In 1939, Shohat extended these ideas introducing a new class of orthogonal polynomials. In fact, he studied orthogonal polynomials associated with forms satisfying the last equation, with no restrictions in the degrees of the polynomials A, and B. Obviously, orthogonal polynomials defined as above, generalize in a natural way the ...

Using the theory of exponential Riordan arrays and orthogonal polynomials, we demonstrate that the Eulerian polynomials and the shifted Eulerian polynomials are moment sequences for a simple family of orthogonal polynomials. The coefficient arrays of these families of orthogonal polynomials are shown to be exponential Riordan arrays. Using the theory of orthogonal polynomials we are then able t...