Extending commuting functions

Special functions and q-commuting variables

This paper is mostly a survey, with a few new results. The first part deals with functional equations for q-exponentials, q-binomials and q-logarithms in q-commuting variables and more generally under q-Heisenberg relations. The second part discusses translation invariance of Jackson integrals, q-Fourier transforms and the braided line. Last modified: August 26, 1996 Note: Report No. 1, Institu...

Differential Operators Commuting with Invariant Functions

Self-commuting Lattice Polynomial Functions on Chains

We provide sufficient conditions for a lattice polynomial function to be self-commuting. We explicitly describe self-commuting polynomial functions on chains.

Extending n-Convex Functions

We are given data α1, . . . , αm and a set of points E = {x1, . . . , xm}. In this paper we address the question of conditions ensuring the existence of a function f satisfying the interpolation conditions f(xi) = αi, i = 1, . . . ,m, that is also n-convex on a set properly containing E. We consider both one point extensions of E, and extensions of E to all of IR. We also determine bounds on n-...

Commuting Functions with No Common Fixed Points)

Introduction. Let/and g be continuous functions mapping the unit interval / into itself which commute under functional composition, that is, f(g(x)) = g(f(x)) for all x in /. In 1954 Eldon Dyer asked whether/and g must always have a common fixed point, meaning a point z in / for which f(z) = z=g(z). A. L. Shields posed the same question independently in 1955, as did Lester Dubins in 1956. The p...