On 𝐿¹ convergence of Fourier series with quasi-monotone coefficients

Autor:	J. W. Garrett, C. S. Rees, Č. V. Stanojević
Rok vydání:	1978
Předmět:	Discrete-time Fourier transform Applied Mathematics General Mathematics Fourier sine and cosine series Function series Fourier inversion theorem Mathematical analysis Parseval's theorem symbols.namesake Fourier analysis Conjugate Fourier series symbols Fourier series Mathematics
Zdroj:	Proceedings of the American Mathematical Society. 72:535-538
ISSN:	1088-6826 0002-9939
DOI:	10.1090/s0002-9939-1978-0509250-5
Popis:	For the class of Fourier series with quasi-monotone coefficients, it is proved that ‖ s n − σ n ‖ = o ( 1 ) , n → ∞ \left \| {{s_n} - {\sigma _n}} \right \| = o(1),n \to \infty , if and only if a n lg ⁡ n = o ( 1 ) , n → ∞ {a_n}\lg n = o(1),n \to \infty . This generalizes a theorem for monotone coefficients and provides a new proof for a result due to Telyakovskii and Fomin.
Databáze:	OpenAIRE
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