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Moment vanishing problem and positivity: Some examples |
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| Authors: | JP Francoise F Pakovich Y Yomdin W Zhao |
| Institution: | aLaboratoire J.-L. Lions, Université P.-M. Curie, Paris 6, 4 Pl. Jussieu, Paris, 75252 France;bDepartment of Mathematics, Beer-Sheva University, Beer-Sheva 84752, Israel;cDepartment of Mathematics, The Weizmann Institute of Science, Rehovot 76100, Israel;dDepartment of Mathematics, Illinois State University, IL 61790-4520, USA |
| 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] and 35] and in other publications in connection with the vanishing problem for differential operators and with the Jacobian conjecture:Conjecture A. For positive μ ifmk(P,1)=0fork=1,2,… , thenmk(P,q)=0fork?1for any q. |
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