Fractional Fourier Series on the Torus and Applications

Autor:	Chen Wang, Xianming Hou, Qingyan Wu, Pei Dang, Zunwei Fu
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	fractional Fourier series fractional approximate identity fractional Fejér kernel fractional Fourier inversion convergence Thermodynamics QC310.15-319 Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Fractal and Fractional, Vol 8, Iss 8, p 494 (2024)
Druh dokumentu:	article
ISSN:	2504-3110
DOI:	10.3390/fractalfract8080494
Popis:	This paper introduces the fractional Fourier series on the fractional torus and proceeds to investigate several fundamental aspects. Our study includes topics such as fractional convolution, fractional approximation, fractional Fourier inversion, and the Poisson summation formula. We also explore the relationship between the decay of its fractional Fourier coefficients and the smoothness of a function. Additionally, we establish the convergence of the fractional Féjer means and Bochner–Riesz means. Finally, we demonstrate the practical applications of the fractional Fourier series, particularly in the context of solving fractional partial differential equations with periodic boundary conditions, and showcase the utility of approximation methods on the fractional torus for recovering non-stationary signals.
Databáze:	Directory of Open Access Journals
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