On L1- Convergence of Certain Trigonometric Sums With Semi-Convex Coefficients

Abstract

The present dissertation entitled,\On L1-Convergence of Certain Trigono- metric Sums With Semi-Convex Coe cients" embodies a brief account of investigations carried out by various authors and by me on L1-convergence of trigonometric series under the supervision of Dr. S.S.Bhatia, Professor, School of Mathematics and Computer Applications, Thapar University, Patiala. The aim of this work is, to study some classes of sequences formed by coe cients of real trigonometric series and to obtain results on L1-convergence of Trigonometric Series with special coe cients. The work reported in this dissertation has been divided into four chapters . The rst chapter is introductory. In this chapter, apart from setting up the notations and terminology to be used in sequel, we have presented some known results interrelated to our results alongwith a brief plan of our results presented in the subsequent chapters. The purpose of chapter II is to study the L1-convergence of modi ed sine sums introduced by Kulwinder Kaur [2003] with semi-convex coe - cients. In chapter III, we have studied the L1-convergence of the sine and cosine trigonometric sums introduced by Xhevat Z.Krasniqi [2009] with semi-convex class of coe cient sequences. We have also studied the necessary and su cient conditions for the L1-convergence of sine and cosine trigonometric series in this chapter. In chapter IV, we have obtained the L1-convergence of the sine and cosine trigonometric sums given by Ram and Kumari [1989] with semi-convex coe cients. Further in this chapter, we have also obtained the necessary and su cient conditions for the L1-convergence of sine and cosine trigonometric series. Towards the end, references of various publications cited in the present dissertation have been reported.