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Pythagorean harmonic summability of Fourier series

Pythagorean harmonic summability of Fourier series

Abstract This paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with the introduction of new concepts like the smoothing operator and semi-harmonic summation. The smoothing operator is demonstrated to be Kalman filtering for linear summability, logistic …