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Izv. RAN. Ser. Mat., 2017, Volume 81, Issue 1, Pages 183–202 (Mi izv8394)  

On Fourier coefficients of functions with respect to general orthonormal systems

V. Sh. Tsagareishvili

Tbilisi Ivane Javakhishvili State University

Abstract: We present results describing some properties of the Fourier coefficients of functions with respect to general orthonormal systems (ONS). We note that good differential properties of the functions do not ensure the ‘good’ behaviour of the Fourier coefficients (in the sense of convergence to zero) of these functions with respect to general ONS. We find conditions on the functions $\varphi_n(x)$ forming an ONS ($\varphi_n(x))$, $n=1,2,…$, for which the series of Fourier coefficients of the functions $f(x)$, where $f'(x)\in V(0,1)$, are absolutely convergent. We consider relationships between ONS, that is, problems of absolute independence for orthonormal systems.

Keywords: Fourier coefficients, absolute convergence, absolutely independent ONS.

DOI: https://doi.org/10.4213/im8394

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English version:
Izvestiya: Mathematics, 2017, 81:1, 179–198

Bibliographic databases:

UDC: 517.521
MSC: Primary 42A16; Secondary 42A20, 42A65
Received: 20.04.2015
Revised: 05.01.2016

Citation: V. Sh. Tsagareishvili, “On Fourier coefficients of functions with respect to general orthonormal systems”, Izv. RAN. Ser. Mat., 81:1 (2017), 183–202; Izv. Math., 81:1 (2017), 179–198

Citation in format AMSBIB
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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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