On the number of zeros of iterated operators on analytic Legendre expansions
Files
TR Number
Date
2001-01-01
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Hindawi
Abstract
Let L=(1−z2)D2−2zD, D=d/dz and f(z)=∑n=0∞cnpn(z), with Pn being the nth Legendre polynomialand f analytic in an ellipse with foci ±1. Set Lk=L(Lk−1), k≥2. Then the number of zeros of Lkf(z) in this ellipse is O(klnk).
Description
Keywords
Citation
Carl Prather, “On the number of zeros of iterated operators on analytic Legendre expansions,” International Journal of Mathematics and Mathematical Sciences, vol. 28, no. 8, pp. 461-467, 2001. doi:10.1155/S0161171201006056