Fourier–Laplace transforms and related questions on certain analytic varieties in C2

For an analytic variety Vϕ = {(z1, z2) ∈ C2: ϕ(z1, z2) = 0}, defined by a holomorphic function ϕ, we assume that the point 0 ∈ Vϕ and that Vϕ −{0} is smooth. In this setting, we construct holomorphic differentials θ, on Vϕ − {0}, with prescribed certain of the values of the integrals zk1 zl2 θ(z1, z2), taken over closed curves on Vϕ which surround 0. The construction is quite explicit and is based on a residue process.We also study similar questions with specific choices of ϕ, in which cases we obtain more complete results.  2005 Elsevier Inc. All rights reserved.