In Inverse Problem for Trigonometric Polynomials: Does the Distribution of a Homogeneous Polynomial in a Gaussian Random Point Define the Polynomial?

In Inverse Problem for Trigonometric Polynomials: Does the Distribution of a Homogeneous Polynomial in a Gaussian Random Point Define the Polynomial?

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.

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Veröffentlicht in:Advances in applied mathematics 1994-09, Vol.15 (3), p.336-359
Hauptverfasser: Baryshnikov, Y.M., Stadje, W.
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Fourier analysis
Functions of a complex variable
Mathematical analysis
Mathematics
Sciences and techniques of general use
Special functions
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Beschreibung
Zusammenfassung: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.
ISSN:0196-8858
1090-2074
DOI:10.1006/aama.1994.1012