On the absolute convergence of Fourier series and generalisation of Lipschitz spaces, defined by differences of fractional order | Zendy

B.I. Peleshenko | Zendy; T.N. Semirenko | Zendy

Open Access

On 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 $\alpha$ ($0 < \alpha < 1$).

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