Moment vanishing problem and positivity: Some examples

J. P. Francoise, F. Pakovich, Y. Yomdin, W. Zhao

Research output: Contribution to journalArticlepeer-review

23 Scopus citations

Abstract

We consider the problem of vanishing of the moments. with Ω a compact domain in Rn and P(x), q(x) complex polynomials in x∈Ω (MVP). The main stress is on relations of this general vanishing problem to the following conjecture which has been studied recently in Mathieu (1997) [22], Duistermaat and van der Kallen (1998) [17], Zhao (2010) [34,35] and in other publications in connection with the vanishing problem for differential operators and with the Jacobian conjecture:. Conjecture AFor positive We recall recent results on one-dimensional (MVP) obtained in Muzychuk and Pakovich (2009) [24], Pakovich (2009,2004) [25,26], Pakovich (preprint) [28] and prove some initial results in several variables, stressing the role of the positivity assumption on the measure μ On this base we analyze some special cases of Conjecture A and provide in these cases a complete characterization of the measures μ for which this conjecture holds.

Original languageEnglish
Pages (from-to)10-32
Number of pages23
JournalBulletin des Sciences Mathematiques
Volume135
Issue number1
DOIs
StatePublished - 1 Jan 2011

ASJC Scopus subject areas

  • General Mathematics

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