Lebesgue Constants and Approximation of Classes of Functions with Bounded Derivative by Polynomials

Roald M. Trigub and Eduard S. Bellinsky
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Roald M. Trigub: Donetsk National University
Eduard S. Bellinsky: University of West Indies

Chapter Chapter 9 in Fourier Analysis and Approximation of Functions, 2004, pp 393-428 from Springer

Abstract: Abstract The norms of multiplier operators are called the Lebesgue constants. In the case of the space C(𝕋m) (or L(𝕋m)) the Lebesgue constants are represented by the integrals $$ {(2\pi )^{ - m}}\int\limits_{{T^m}} {\left| {\sum\limits_k {{\lambda _{n,k}}{e^{i(k,x)}}} } \right|dx} $$ .

Keywords: Fourier Series; Convex Body; Lower Estimate; Absolute Constant; Lebesgue Constant (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-1-4020-2876-2_9

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