Lebesgue constants for Jacobi expansions
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- by Donald I. Cartwright PDF
- Proc. Amer. Math. Soc. 87 (1983), 427-433 Request permission
Abstract:
Sharp estimates are given for the Lebesgue constants $|||{s_n}||{|_p} = \sup \left \{ {{{\left \| {{s_n}f} \right \|}_p}:f \in L_w^p,{{\left \| f \right \|}_p} \leqslant 1} \right \}$ 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 $[ - 1,1]$.References
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Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 87 (1983), 427-433
- MSC: Primary 42C10; Secondary 33A65
- DOI: https://doi.org/10.1090/S0002-9939-1983-0684632-1
- MathSciNet review: 684632