Abstract:
The Fourier series, known for expressing functions as sums of sines and cosines, can be refined in various ways to improve convergence and achieve more accurate signal approximation. Utilizing a product transform increases the convergence rate, resulting in a closer representation of the original signal. In this work, we introduce the notion of Euler-Banach operator to approximate functions in the Lebesgue class through the Fourier series and its conjugate series and also to establish two approximation theorems using our proposed summation operator.
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