CLASSES OF $L^1$-CONVERGENCE OF FOURIER SERIES
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 22
DOI: https://doi.org/10.56827/SEAJMMS.2024.2001.35
Author :
Sandeep Kaur Gill (Department of Applied Sciences, GNDEC, Ludhiana, Punjab, INDIA)
Jatinderdeep Kaur (School of Mathematics, TIET, Patiala, Punjab, INDIA)
S. S. Bhatia (School of Mathematics, TIET, Patiala, Punjab, INDIA)
Abstract
In this paper, wider classes of Fourier cosine series are introduced and found that $a_n \log n = o(1), ~ n \rightarrow \infty$ is a necessary and sufficient condition for $L^1$-convergence. Our results generalize the results obtained by A.N. Kolmogorov as well as R. Bala and B. Ram for cosine series while our new classes $\mathcal{JS}$ quasi convex and $\mathcal{JS}$ semi convex are the extensions of the classes quasi convex null sequence and semi convex respectively.
Keywords and Phrases
Dirichlet kernel, conjugate Dirichlet kernel, Fejer kernel, conjugate Fejer kernel, $L^1$- convergence.
A.M.S. subject classification
42A16, 42A20, 42A32.
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