Open AccessOn the absolute convergence of Fourier series and generalisation of Lipschitz spaces, defined by differences of fractional order
Author(s) -
B.I. Peleshenko,
T.N. Semirenko
Publication year - 2016
Publication title -
researches in mathematics
Language(s) - English
Resource type - Journals
eISSN - 2664-5009
pISSN - 2664-4991
DOI - 10.15421/241613
Subject(s) - lipschitz continuity , fourier series , mathematics , absolute convergence , series (stratigraphy) , order (exchange) , convergence (economics) , fourier transform , omega , mathematical analysis , fractional calculus , fourier analysis , conjugate fourier series , alpha (finance) , pure mathematics , physics , statistics , short time fourier transform , paleontology , finance , quantum mechanics , economics , biology , economic growth , construct validity , psychometrics
We obtain the necessary and sufficient conditions in terms of Fourier coefficients of $2\pi$-periodic functions $f$ with absolutely convergent Fourier series, for $f$ to belong to the generalized Lipschitz classes $H^{\omega, \alpha}_{\mathbb{C}}$, and to have the fractional derivative of order $\alpha$ ($0 < \alpha < 1$).