On L1- Convergence of Certain Trigonometric Sums

Abstract

The present dissertation entitled,\On L1-Convergence of Certain Trigonomet- ric Sums" contains a brief account of investigations carried out by various authors and by me on L1-convergence of trigonometric series under the supervision of Dr. Jatinderdeep Kaur, Lecturer and Dr. S.S.Bhatia, Professor, School of Mathematics and Computer Applications, Thapar University, Patiala. The work presented 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 along with 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 cosine sums introduced by C.S. Rees and C.V. Stanajevi c in 1973 with class S of coe cient sequences. In chapter III, we have studied the L1-convergence of the modi ed cosine sums given by Suresh Kumari and Babu Ram in 1987 with class S. In chapter IV, we have obtained the L1-convergence of the cosine sums given by Ram and Kumari with class Sr of Tomovski. We have also obtained the L1-convergence of the rth derivative of the cosine sums with Sr class. Towards the end, references of various publications cited in the present dissertation have been reported.