Analytic central extensions of infinite dimensional white noise *--Lie algebras

The connection between the $*$--Lie algebra of the Renormalized Higher Powers of White Noise (RHPWN) and the centerless Virasoro (or Witt)-Zamolodchikov-$w_{\infty}$ $*$--Lie algebra of conformal field theory, as well as the associated Fock space construction, have recently been established (\cite{1}--\cite{4}). In this paper we describe a method for looking for a special class of central extensions of the RHPWN and $w_{\infty}$ $*$--Lie algebras called "analytic", i.e. central extensions where the defining cocycles can be written as formal power series of the indices of the RHPWN and $w_{\infty}$ generators. Our method is also applied to the well known Virasoro central extension of the Witt algebra.