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Proceedings of the American Mathematical Society

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Lebesgue constants for Jacobi expansions


Author: Donald I. Cartwright
Journal: Proc. Amer. Math. Soc. 87 (1983), 427-433
MSC: Primary 42C10; Secondary 33A65
MathSciNet review: 684632
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Abstract: Sharp estimates are given for the Lebesgue constants $ \vert\vert\vert{s_n}\vert\vert{\vert _p} = \sup \left\{ {{{\left\Vert {{s_n}f} \right\Vert}_p}:f \in L_w^p,{{\left\Vert f \right\Vert}_p} \leqslant 1} \right\}$ for $ p$ outside the Pollard interval $ ({p'_0},{p_0})$, where $ {s_n}f$ is the $ n$th partial sum of the Jacobi expansion of a function $ f$ which is in the $ {L^p}$ space with respect to the weight $ w(x) = {(1 - x)^\alpha }{(1 + x)^\beta }$ on $ [ - 1,1]$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0684632-1
Keywords: Jacobi polynomials, Lebesgue constants, compact symmetric spaces of rank one
Article copyright: © Copyright 1983 American Mathematical Society