TY - JOUR
T1 - Moment vanishing problem and positivity
T2 - Some examples
AU - Francoise, J. P.
AU - Pakovich, F.
AU - Yomdin, Y.
AU - Zhao, W.
N1 - Funding Information:
✩ This research was supported by the ISF, Grants No. 979/05 and NEW/09, by the IMOS France–Israel Research grant, by the Minerva foundation, by NSA Grant H98230-10-1-0168, and by the ANR BLAN07-2-182920. * Corresponding author. E-mail addresses: [email protected] (J.P. Francoise), [email protected] (F. Pakovich), [email protected] (Y. Yomdin), [email protected] (W. Zhao).
PY - 2011/1/1
Y1 - 2011/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=78751568127&partnerID=8YFLogxK
U2 - 10.1016/j.bulsci.2010.06.002
DO - 10.1016/j.bulsci.2010.06.002
M3 - Article
AN - SCOPUS:78751568127
SN - 0007-4497
VL - 135
SP - 10
EP - 32
JO - Bulletin des Sciences Mathematiques
JF - Bulletin des Sciences Mathematiques
IS - 1
ER -