Multivariate delta GonCarov and Abel polynomials Academic Article uri icon


  • 2016 Elsevier Inc. Classical Gonarov polynomials are polynomials which interpolate derivatives. Delta Gonarov polynomials are polynomials which interpolate delta operators, e.g., forward and backward difference operators. We extend fundamental aspects of the theory of classical bivariate Gonarov polynomials and univariate delta Gonarov polynomials to the multivariate setting using umbral calculus. After introducing systems of delta operators, we define multivariate delta Gonarov polynomials, show that the associated interpolation problem is always solvable, and derive a generating function (an Appell relation) for them. We show that systems of delta Gonarov polynomials on an interpolation grid ZRd are of binomial type if and only if Z=ANd for some dd matrix A. This motivates our definition of delta Abel polynomials to be exactly those delta Gonarov polynomials which are based on such a grid. Finally, compact formulas for delta Abel polynomials in all dimensions are given for separable systems of delta operators. This recovers a former result for classical bivariate Abel polynomials and extends previous partial results for classical trivariate Abel polynomials to all dimensions.

published proceedings


altmetric score

  • 0.25

author list (cited authors)

  • Lorentz, R., Tringali, S., & Yan, C. H.

citation count

  • 1

complete list of authors

  • Lorentz, Rudolph||Tringali, Salvatore||Yan, Catherine H

publication date

  • January 2017