Differential identities

Beauzamy, Bernard; Dégot, Jérôme

doi:10.1090/S0002-9947-1995-1277095-1

Differential identities
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by Bernard Beauzamy and Jérôme Dégot

Trans. Amer. Math. Soc. 347 (1995), 2607-2619

DOI: https://doi.org/10.1090/S0002-9947-1995-1277095-1

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Abstract:

We deal here with homogeneous polynomials in many variables and their hypercube representation, introduced in [5]. Associated with this representation there is a norm (Bombieri’s norm) and a scalar product. We investigate differential identities connected with this scalar product. As a corollary, we obtain Bombieri’s inequality (originally proved in [4]), with significant improvements. The hypercube representation of a polynomial was elaborated in order to meet the requests of massively parallel computation on the "Connection Machine" at Etablissement Technique Central de l’Armement; we see here once again (after [3] and [5]) the theoretical power of the model.

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