General Periodic Functions and Generalization of Fourier analysis
Author: Mykola Yaremenko
Abstract: In this paper, we consider $$l_{p}-$$ periodical functions $$ pcs (m θ) $$ and $$ psn (m θ) $$, which are defined on a curve given by an equation $$ |x|^p + |y|^p= 1 $$ on $$ R^2$$ as functions of its length. Considering $$ pcs (m θ) $$ and $$ psn (m θ) $$ as an independent functional system, we construct the theory similar to Fourier analysis with the proper weights. For these weights, we establish an analog of the Riemannian theorem. The adjoint representations are introduced and dual theory is developed. These Fourier representations can be used for approximation for the oscillation processes.
Pages: 103-109
DOI: 10.46300/91019.2022.9.15
International Journal of Pure Mathematics, E-ISSN: 2313-0571, Volume 9, 2022, Art. #15
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