Bezout identities with pseudopolynomial entries

Abstract.

Let $A_p({\Bbb C}^{n-1})$ be the algebra of entire functions in n - 1 variables satisfying some growth conditions (p is a plurisubharmonic weight). We consider p-pseudopolynomials in (z ₁;z ^') = (z ₁; z ₂,..., z _n) in the weighted algebra $A_{\tilde p}({\Bbb C}^n){\tilde p}(z) = (\ln 2+\vert z_1\vert )+ p(z')$ of the form¶¶$f(z)= a_0(z')z_1^m+\sum\limits ^n_{k=1} a_k(z')z_1^{m-k}$¶¶ where $a_0,a_1,\ldots, a_m \in A_p({\Bbb C}^{n-1})$.¶We establish several results concerning solutions of the Bezout identity $1 = q_1 f_1 + \cdots + q_m f_m$ when $f_1 \ldots f_m \in A _{\tilde p}({\Bbb C}^n)$ are “strongly coprime”.