Bezout identities with pseudopolynomial entries

摘要

Let A_p(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 (z1;z') = (z1; z2,..., zn) in the weighted algebra A_p(C~n)p(z) = (In 2+∣z'∣ )+ p(z') of the form f(z)= a_0(z')z_1~m+∑n_(k=1) a_k(z')z_1~(m-k) where a_0,a_1,..., a_m∈A_p(C~(n-1)).