Bernstein polynomials and Milnor algebras.
Let f be an analytic germ on C(n+1). Then there is an analytic linear partial differential operator P with polynomial dependence on s, and a polynomial b(s), such that Pf(s+1) = b(s)f(s). This paper contains a simple existence proof and geometric interpretation in the case when f has an isolated critical zero at the origin, and is contained in its Jacobian ideal of first partial derivatives.
Kochman
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Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138.