Abstract
In trigonometric approximation one can show that smoothness of a function is equivalent to a quick decrease to zero of its error of approximation by trigonometric polynomials. The key steps to show this are the Jackson- and the Bernstein-inequality. In this paper we will investigate some Bernsteintype inequalities concerning conjugate functions and Laplacian. In a forthcoming paper we will show that these inequalities imply the equivalence of the order of approximation by the classical Jackson operator (in higher dimension) and a corresponding measure for the smoothness of the function.
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Knoop, HB., Zhou, X. (1999). Some Inequalities for Trigonometric Polynomials and their Derivatives. In: Müller, M.W., Buhmann, M.D., Mache, D.H., Felten, M. (eds) New Developments in Approximation Theory. ISNM International Series of Numerical Mathematics, vol 132. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8696-3_6
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DOI: https://doi.org/10.1007/978-3-0348-8696-3_6
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9733-4
Online ISBN: 978-3-0348-8696-3
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