ANALYTIC FUNCTIONALS ANNIHILATED BY IDEALS

Let V be a n-dimensional Stein manifold, I be a closed ideal of holomo rphic functions on V. It was proved by Roger Gay that, given an analyt ic functional T such that hT = 0 (as a functional) for any h is an ele ment of I, one can find some (n, n) compactly supported current (T) ov er tilde, such that (T) over tilde(phi) = 0 for any phi is an element of IE(0,0)(V) and T(h) = (T) over tilde(h) for any h analytic on V. In this paper, we give some explicit construction of (T) over tilde in t erms of residual currents when I is defined as a complete intersection or is locally Cohen-Macaulay. Moreover, by means of integral represen tation formulas of the Andersson-Berndtsson-Passare type, we also stud y the non complete intersection case in order to represent analytic fu nctionals orthogonal to the ideal in terms of currents annihilated (as currents) by some power (less than n) of the local integral closure o f IE(0,0)(V).