Abstract
In this article we obtain a factorization theorem for the functions in Paatero’s V ( k ) V(k) space. We bring attention to a significant result of Pinchuk which unfortunately is false. This result relates measures associated to functions in V ( k ) V(k) and an integral representation theorem for such functions. We prove necessary and sufficient conditions for a wide class of functions (in particular, the polynomials) to belong to the Paatero class based on the geometry of their critical points, and obtain explicit representation of the measures associated to a wide class of such polynomials that includes the Suffridge polynomials.
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