Browsing Scholarly Works, Department of Mathematics by Author "Prather, Carl"
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On the number of zeros of iterated operators on analytic Legendre expansions
(Hindawi, 2001-01-01)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).
