David E. Grow

Brownian Motion Indexed by a Time Scale

In this article, we generalize Wieners existence result for one-dimensional Brownian motion by constructing a suitable continuous stochastic process where the index set is a time scale. We construct a countable dense subset of a time scale and use it to prove a generalized version of the Kolmogorov–Čentsov theorem. As a corollary, we obtain a local Hölder-continuity result for the sample paths of generalized Brownian motion indexed by a time scale.

The independence of characters on non-abelian groups

We show that there are characters of compact, connected, non-abelian groups that approximate random choices of signs. The work was motivated by Kroneckers theorem on the independence of exponential functions and has applications to thin sets.

CENTRAL INTERPOLATION SETS FOR COMPACT GROUPS AND HYPERGROUPS

We prove that every infinite subset of the dual of a compact, connected group contains an infinite, central, weighted I0 set. This yields a new proof of the fact that the duals of such groups admit infinite central p-Sidon sets for each p > 1. We also establish the existence of infinite, weighted I0 sets in the duals of many compact, abelian hypergroups. 2000 Mathematics Subject Classification. Primary 43A46; secondary 43A62, 43A30.

Mathematical analysis of the complete iterative inversion method — I

A gas composed of identical isotropic molecules has a potential energy of interaction between pairs of particles that depends only on their separation distance. The pair potential is encoded in the virial coefficients of the virial equation of state for a gas.The complete iterative inversion method is a technique employed in an attempt to recover the pair potential from the second virial coefficient. Implicit in the complete iterative inversion method is the requirement that various mathematical expressions are meaningful: improper integrals converge, derivatives exist, etc.We provide a mathematical framework in which all these implicit assumptions are valid. We show that the complete iterative inversion method cannot recover the pair potential even if the target potential and the initial estimate are infinitely differentiable.

Representations of Fourier Coefficients in Tauberian L1-convergence Classes

Abstract It is shown that the Fourier coefficients satisfying Stanojevics Tauberian condition can be represented in terms of O-regularly varying sequences.