Global Journal of Pure and Applied Mathematics
  • Year: 2006
  • Volume: 2
  • Issue: 2

On L1-Convergence of Certain Trigonometric Sums

  • Author:
  • S.S. Bhatia, Jatinderdeep Kaur
  • Total Page Count: 6
  • Page Number: 111 to 116

School of Mathematics & Computer Applications, Thapar Institute of Engg. & Tech., (Deemed University), Patiala (Punjab)-147004, INDIA.

*E-mail: ssbhatia63@yahoo.com

**E-mail: jatinkaur4u@yahoo.co.in

AMS Subject Classification: Primary 42A20, Secondary 42A32.

Abstract

In this paper, a generalization of a theorem of Hooda and Ram on L1-convergence of modified cosine sums introduced by Kumari and Ram has been proved by considering the more general class of sequences S** instead of the class S* of coefficient sequences. Also, a necessary and sufficient condition for the L1-convergence of the cosine series is deduced as a corollary. These results also generalize the results of Teljakovskii on L1-convergence of the cosine series.

Keywords

L1-convergence, modified cosine sums, quasimonotone, Dirichlet kernel