IJMMSInternational Journal of Mathematics and Mathematical Sciences1687-04250161-1712Hindawi Publishing Corporation38674510.1155/S0161171201006056On the number of zeros of iterated operators on analytic Legendre expansionsPratherCarlcprather@vt.eduDepartment of MathematicsVirginia TechBlacksburg, VA 24061-0123USAvt.edu200106122001288461467100920002001Copyright © 2001 Hindawi Publishing Corporation

Let L=(1z2)D22zD, D=d/dz and f(z)=n=0cnpn(z), with Pn being the nth Legendre polynomial and f analytic in an ellipse with foci ±1. Set Lk=L(Lk1), k2. Then the number of zeros of Lkf(z) in this ellipse is O(klnk).