IN INVERSE PROBLEM FOR TRIGONOMETRIC POLYNOMIALS - DOES THE DISTRIBUTION OF A HOMOGENEOUS POLYNOMIAL IN A GAUSSIAN RANDOM POINT DEFINE THE POLYNOMIAL

Abstract

It is shown that the probability distribution of the value of a homogeneous polynomial in two Gaussian variables determines the polynomial up to some explicitly described ambiguity, if the degree of the polynomial is five or less, or for generic polynomials of arbitrary degree. (C) 1994 Academic Press, Inc.