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A FAMILY OF HEAT FUNCTIONS AS SOLUTIONS OF INDETERMINATE MOMENT PROBLEMS
 

Summary: A FAMILY OF HEAT FUNCTIONS AS SOLUTIONS OF
INDETERMINATE MOMENT PROBLEMS
RICARDO G´OMEZ AND MARCOS L´OPEZ-GARC´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: log-normal, generalized Stieltjes-Wigert and q-Laguerre.
1. Introduction
For a real-valued, 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 real-valued, 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 M-determinate.
Otherwise the moment problem is said to be M-indeterminate. When
we replace N with Z we can formulate the same problem (the so-called

  

Source: Aíza, Ricardo Gómez - Instituto de Matemáticas, Universidad Nacional Autónoma de México

 

Collections: Mathematics