On approximation of continuous functions by trigonometric polynomials

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Abstract

We generalize the classical Jackson–Bernstein constructive description of Hölder classes of periodic functions on the interval [π,π]. We approximate by trigonometric polynomials continuous functions defined on a compact set E[π,π]. This set may consist of an infinite number of intervals.

Keywords

Trigonometric polynomial
Green’s function
Levin’s function
Approximation

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