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

T. Xie, S. Zhou
1992 Colloquium Mathematicum  
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
more » ... best approximations in L p space; the paper [1] contains the following theorem: j=0 , is a given sequence of real distinct (by a = b we mean that a ≡ b (mod 2π)) nodes and {λ n } is any given positive decreasing sequence. Then there exists an infinitely differentiable function f with period 2π such that
doi:10.4064/cm-63-2-323-328 fatcat:f7baycbjajf3tcg4s6op5rb7o4