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

Carl Prather

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 28, 1-7

Abstract:

Let L = ( 1 − z 2 ) D 2 − 2 z D , D = d / d z and f ( z ) = ∑ n = 0 ∞ c n p n ( z ) , with P n being the n th Legendre polynomial and f analytic in an ellipse with foci ± 1 . Set L k = L ( L k − 1 ) , k ≥ 2 . Then the number of zeros of L k f ( z ) in this ellipse is O ( k ln k ) .

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:386745

DOI: 10.1155/S0161171201006056

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