Unconditional Convergence of General Fourier Series

L. Gogoladze ; V. Tsagareishvili

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 83-93.

Résumé

We consider problems of unconditional convergence of Fourier series of $\operatorname {Lip}1$ functions with respect to general orthonormal systems (ONSs). Sufficient conditions on the functions of an ONS are found under which the Fourier series of every $\operatorname {Lip}1$ function with respect to this system converges unconditionally. We show that some of the obtained results are sharp. We also prove that from any ONS $(\varphi _n)$ one can extract a subsequence $(\varphi _{n_k})$ with respect to which the Fourier series of every $\operatorname {Lip}1$ function converges unconditionally.

Détail

Keywords: orthonormal system, Fourier series, unconditional convergence
Mots-clés : Fourier coefficients.

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