Integrability and L1-convergence of cosine trigonometric series with special coefficients

Abstract

The present dissertation entitled, “Integrability and L1 -Convergence of Cosine trigonometric Series with special coefficients”, contains a brief account of investigations carried out by me on L1convergence of trigonometric cosine series under the supervision of Dr. Jatinderdeep Kaur, Assistant Professor, School of Mathematics and Computer Applications, Thapar University, Patiala. The work presented in this dissertation has been divided into three chapters. The first chapter is introductory. In this chapter, apart from setting up the notations and terminology to be used in sequel, we have presented some well-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 integrability and L1-convergence of cosine trigonometric series under the Class S of Sidon and Telyakovskii. In chapter III, I have studied the results concerning the L1convergence of modified cosine sums introduced by C.S. Rees and C.V. Stanojevic by using Cesaro means of integral and non-integral orders and obtained L1convergence Of Fourier cosine series as corollary. Towards the end, references of various publications cited in the present dissertation have been reported.