In this paper we study the regularity properties of two maximal operators of convolution type:
the heat flow maximal operator (associated to the Gauss kernel) and the Poisson maximal …

We establish a new formula for the heat kernel on regular trees in terms of classical I I-
Bessel functions. Although the formula is explicit, and a proof is given through direct …

By a discrete torus we mean the Cayley graph associated to a finite product of finite cycle
groups with the generating set given by choosing a generator for each cyclic factor. In this …

In this paper we present a general unifying principle for computing finite trigonometric sums
of types that arise in physics and number theory. We obtain formulas that are more general …

In this paper we develop the parametrix approach for constructing the heat kernel on a
graph G. In particular, we highlight two specific cases. First, we consider the case when G is …

In this article we develop a general method by which one can explicitly evaluate certain
sums of n th powers of products of d≥ 1 elementary trigonometric functions evaluated at …

In this paper, we establish relations between special values of Dirichlet L-functions and
those of spectral zeta functions or L-functions of cycle graphs. In fact, they determine each …

This paper illustrates the utility of the heat kernel on Z as the discrete analogue of the
Gaussian density function. It is the two-variable function KZ (t, x)= e− 2tIx (2t) involving a …

This thesis concerns combinatorial and geometric group theory—the interplay between the
properties of groups and those of the geometric objects on which they act. More specifically …

We extend a certain type of identities on sums of I-Bessel functions on lattices, previously
given by G. Chinta, J. Jorgenson, A. Karlsson and M. Neuhauser. Moreover we prove that …