On the number of zeros of iterated operators on analytic Legendre expansionsReportar como inadecuado




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

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

Received 10 September 2000

Copyright © 2001 Hindawi Publishing Corporation. 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.

Abstract

Let L=1−z2D2−2zD, D=d-dz and fz=∑n=0∞cnpnz, with Pn being the nth Legendre polynomialand f analytic in an ellipse with foci ±1. Set Lk=LLk−1, k≥2. Then the number of zeros of Lkfz in this ellipse is Oklnk.





Autor: Carl Prather

Fuente: https://www.hindawi.com/



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