An inequality for products of polynomials

Author:
Bruce Reznick

Journal:
Proc. Amer. Math. Soc. **117** (1993), 1063-1073

MSC:
Primary 11E76; Secondary 26C05

MathSciNet review:
1119265

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Abstract: Beauzamy, Bombieri, Enflo, and Montgomery recently established an inequality for the coefficients of products of homogeneous polynomials in several variables with complex coefficients (forms). We give this inequality an alternative interpretation: let be a form of degree , let denote the associated order differential operator, and define by . Then for all forms and , regardless of degree or number of variables. Our principal result is that if and only if, after a unitary change of variables, and are forms in disjoint sets of variables. This is achieved via an explicit formula for in terms of the coefficients of and .

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DOI:
https://doi.org/10.1090/S0002-9939-1993-1119265-2

Article copyright:
© Copyright 1993
American Mathematical Society