Equivalence of a 𝐾-functional with the approximation behavior of some linear means for abstract Fourier series

Trebels, Walter

doi:10.1090/S0002-9939-99-05265-X

Equivalence of a $K$-functional with the approximation behavior of some linear means for abstract Fourier series
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Proc. Amer. Math. Soc. 127 (1999), 2883-2887 Request permission

Abstract:

Within the setting of abstract Cesàro-bounded Fourier series a $K$-functional is introduced and characterized by the convergence behavior of some linear means. Applications are given within the framework of Jacobi, Laguerre and Hermite expansions. In particular, Ditzian’s (1996) equivalence result in the setting of Legendre expansions is covered.

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