On approximation of continuous functions by trigonometric polynomials Original Research Article

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