International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 8, Pages 461-467

On the number of zeros of iterated operators on analytic Legendre expansions

Carl Prather

Department of Mathematics, Virginia Tech, Blacksburg 24061-0123, VA, USA

Received 10 September 2000

Copyright © 2001 Carl Prather. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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).