Integrals of logarithmic forms on semi-algebraic sets and a generalized Cauchy formula, Part I: convergence theorems

Abstract

In this paper consisting of two parts, we study the integral of a logarithmic differential form on a compact semi-algebraic set in R^n or C^n. In Part I, we prove the convergence of the integral when the semi-algebraic set satisfies allowability (or admissibility), a condition on the dimension of the intersection of the set and the pole divisor of the differential form.

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• Integrals of logarithmic forms on semi-algebraic sets and a generalized Cauchy formula Part II: generalized Cauchy formula