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