Geodesic
Unconditional Convergence of General Fourier Series
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 83-93

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: orthonormal system, Fourier series, unconditional convergence
Mots-clés : Fourier coefficients. 
@article{TM_2022_319_a6,
     author = {L. Gogoladze and V. Tsagareishvili},
     title = {Unconditional {Convergence} of {General} {Fourier} {Series}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {83--93},
     publisher = {mathdoc},
     volume = {319},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2022_319_a6/}
}
TY  - JOUR
AU  - L. Gogoladze
AU  - V. Tsagareishvili
TI  - Unconditional Convergence of General Fourier Series
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2022
SP  - 83
EP  - 93
VL  - 319
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2022_319_a6/
LA  - ru
ID  - TM_2022_319_a6
ER  - 
%0 Journal Article
%A L. Gogoladze
%A V. Tsagareishvili
%T Unconditional Convergence of General Fourier Series
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2022
%P 83-93
%V 319
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2022_319_a6/
%G ru
%F TM_2022_319_a6
L. Gogoladze; V. Tsagareishvili. Unconditional Convergence of General Fourier Series. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Approximation Theory, Functional Analysis, and Applications, Tome 319 (2022), pp. 83-93. http://geodesic.mathdoc.fr/item/TM_2022_319_a6/