Polynomial operators and local smoothness classes on the unit interval

  • Authors:

  • H. N. Mhaskar

  • Affiliations:

  • Department of Mathematics, California State University, Los Angeles, CA 90032, USA

  • Venue:
  • Journal of Approximation Theory
  • Year:
  • 2004

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Abstract

We obtain a characterization of local Besov spaces of functions on [-1,1] in terms of algebraic polynomial operators. These operators are constructed using the coefficients in the orthogonal polynomial expansions of the functions involved. The example of Jacobi polynomials is studied in further detail. A by-product of our proofs is an apparently simple proof of the fact that the Cesaro means of a sufficiently high integer order of the Jacobi expansion of a continuous function are uniformly bounded.