Convergence of Complex Trigonometric Sums in the Metric Space L

Abstract

The present dissertation entitled"Convergence of Complex trigonometri Sums in the metric space L" embodies a brief acocunt of investigations carried out by various authors and by me on L1-convergence of complex trigonometric sums under the supervision of Dr. S.S. Bhatia,Professor and Dr. Jatinderdeep Kaur, Lecturer,School of Mathematics and Computer Applications,Thapar University,Patiala. The aim of this work is,study and obtain some results on L1-convergence of Complex Trigonometric series with special cofficients. The whole work of my dissertation is divided into four chapters.The first chapter is introductory.In this chapter,apart from setting up the notations and terminology to be used in the sequel,I have given a brief account of some results along with a brief plan of results presented in the subsequent chapters.In second chapter,I have studied the"L1-Convergence of Modified Complex Trigonometric Sums"with coefficients belonging to class R*.In chapter third,I have studied the L1-convergence of rth differential of the complex trigonometric sums introduced in second chapter.The aim of chapter four is to study L1-convergence of newly modified complex from of Trigonometric sums with semi-convex coefficients. Towards the end,I have give references of various publications cited in the present dissertation.