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The divergence phenomena of interpolation type operators in $L^p$ space

1992
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Colloquium Mathematicum
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the class of all real continuous functions on [−1, 1]. Denote by C r [−1,1] the space of real functions on [−1, 1] which have r continuous derivatives, and by C ∞ [−1,1] the space of real functions on [−1, 1] which are infinitely differentiable. For f ∈ L p [−1,1] , let E n (f ) p be the best approximation to f by polynomials of degree n in L p space. Our works [1], [5] concern the divergence phenomena of trigonometric Lagrange interpolation approximations in comparison with best approximations

doi:10.4064/cm-63-2-323-328
fatcat:f7baycbjajf3tcg4s6op5rb7o4