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2000 Mathematics Subject Classification: 33D15, 33D90, 39A13In this paper we study the q-heat and q-Poisson’s operators associated
with the q-operator ∆q (see[5]). We begin by summarizing some statements
concerning the q-even translation operator Tx,q, defined by Fitouhi
and Bouzeffour in [5]. Then, we establish some basic properties of the q-heat
semi-group such as boundedness and positivity. In the second part,
we introduce the q-Poisson operator P^t, and address its main properties.
We show...
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