I've seen a lot of proofs of the convergence properties for the Fourier series of continuous periodic functions that use the assumption that the function's derivative and second derivatives exist and are also continuous. I was wondering is the stipulation that the derivatives exist considered not that restrictive of an assumption because we can consider the Stone-Wierstrass polynomial approximation of the function instead which converges uniformly to any continuous function on an interval and does have continuous derivatives?
2026-04-08 19:40:27.1775677227
Question regarding the convergence properties of the Fourier summation
41 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in REAL-ANALYSIS
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