Geodesic
$L^1$-convergence of modified complex trigonometric sums
Lobachevskii journal of mathematics, Tome 12 (2003), pp. 3-10.

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

In this paper we study $L^1$-convergence of modified complex trigonometric sums introduced by Ram and Kumari [2] and obtain a necessary and sufficient condition for $L^1$-convergence of Fourier series under a new class ${\rm K}^*$ of coefficients.
Keywords: $L^1$-convergence of modified complex trigonometric sums, Dirichlet kernel.
Mots-clés : $L^1$-convergence of Fourier series 
@article{LJM_2003_12_a0,
     author = {S. S. Bhatia and K. Kaur and B. Ram},
     title = {$L^1$-convergence of modified complex trigonometric sums},
     journal = {Lobachevskii journal of mathematics},
     pages = {3--10},
     publisher = {mathdoc},
     volume = {12},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2003_12_a0/}
}
TY  - JOUR
AU  - S. S. Bhatia
AU  - K. Kaur
AU  - B. Ram
TI  - $L^1$-convergence of modified complex trigonometric sums
JO  - Lobachevskii journal of mathematics
PY  - 2003
SP  - 3
EP  - 10
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2003_12_a0/
LA  - en
ID  - LJM_2003_12_a0
ER  - 
%0 Journal Article
%A S. S. Bhatia
%A K. Kaur
%A B. Ram
%T $L^1$-convergence of modified complex trigonometric sums
%J Lobachevskii journal of mathematics
%D 2003
%P 3-10
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2003_12_a0/
%G en
%F LJM_2003_12_a0
S. S. Bhatia; K. Kaur; B. Ram. $L^1$-convergence of modified complex trigonometric sums. Lobachevskii journal of mathematics, Tome 12 (2003), pp. 3-10. http://geodesic.mathdoc.fr/item/LJM_2003_12_a0/

[1] Bary N. K., A Treatise on Trigonometric Series, vol. II, Pergamon Press, London, 1964 | Zbl

[2] Ram B. and Kumari S., “On L1-convergence of certain trigonometric sums”, Indian J. Pure Appl. Math., 20 (1989), 908–914 | MR | Zbl

[3] Goldberg R. R. and Stanojevič Č. V., L1-convergence and Segal algebras of Fourier series, preprint, 1980

[4] Sheng S. Y., “The extention of the theorems of Č. V. Stanojevič and V. B. Stanojevič”, Proc. Amer. Math. Soc., 110 (1990), 895–904 | DOI | MR | Zbl