On a Sequence of Fast Decreasing Polynomial Operators

What is it about?

Let f be a piecewise analytic function on the unit interval (respectively, the unit circle of the complex plane). Starting from the Chebyshev (respectively, Fourier) coefficients of f, we construct a sequence of fast decreasing polynomials (respectively, trigonometric polynomials) which “detect” the points where f fails to be analytic, provided f is not infinitely differentiable at these points.

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