S. S. Bhatia, K. Kaur, B. Ram, “<nobr>$L^1$</nobr>-convergence of modified complex trigonometric sums”, Lobachevskii J. Math., 2003, Volume 12,Pages <nobr>3

$L^1$-convergence of modified complex trigonometric sums

S. S. Bhatia^ab, K. Kaur^ba, B. Ram^ab

^a School of Mathematics and Computer Applications, Thapar Institute of Engineering and Technology
^b Maharshi Dayanand University

Abstract: 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, $L^1$-convergence of Fourier series, Dirichlet kernel.

Submitted by: F. G. Avkhadiev
Received: 14.10.2002

Language: English