 
Summary: A FAMILY OF HEAT FUNCTIONS AS SOLUTIONS OF
INDETERMINATE MOMENT PROBLEMS
RICARDO G´OMEZ AND MARCOS L´OPEZGARC´IA
Abstract. We construct a family of functions satisfying the heat
equation and show how they can be used to generate solutions to
indeterminate moment problems. The following cases are consid
ered: lognormal, generalized StieltjesWigert and qLaguerre.
1. Introduction
For a realvalued, measurable function f defined on [0, ) , its nth
moment is defined as sn(f) =
0
xn
f(x)dx, n N = {0, 1, . . .}. Let
(sn)n0 be a sequence of real numbers. If f is a realvalued, measurable
function defined on [0, ) with moment sequence (sn)n0 we say that
f is a solution to the Stieltjes moment problem (related to (sn)n0). If
the solution is unique, the moment problem is called Mdeterminate.
Otherwise the moment problem is said to be Mindeterminate. When
we replace N with Z we can formulate the same problem (the socalled
