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Expositio paper exp-20260820-872577

Infinite Series Through Fourier Analysis

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In this paper, we will introduce Fourier Series through the Orthogonality Relations from which we consider Parseval's Theorem. Then, we wish to extend the concept of Fourier Series of aperiodic functions, specifically showing the Fourier Transform. The usage …

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exp-20260820-872577v1 Latest public version Public since August 20, 2026 Submitted August 20, 2026 0 saves
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Aleksei Lopatin

Abstract

In this paper, we will introduce Fourier Series through the Orthogonality Relations from which we consider Parseval's Theorem. Then, we wish to extend the concept of Fourier Series of aperiodic functions, specifically showing the Fourier Transform. The usage of the Fourier Transform brings curious phenomena as shown by Shannon and Nyquist in their respective papers, which we mention in an example.

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Mathematics
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Abstract harmonic analysis Abstract harmonic analysis Other transforms and operators of Fourier type

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exp-20260820-872577v1

Infinite Series Through Fourier Analysis

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Uploaded Aug 20, 2026 489745 bytes Selected Latest
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