\(L^1\)-convergence of modified complex trigonometric sums. (English) Zbl 1016.42002

Bhatia, S. S.; Kaur, Kulwinder; Ram, Babu

Lobachevskii J. Math. 12, 3-10 (2003).

Summary: In this paper we study \(L^{1}\)–convergence of modified complex trigonometric sums introduced by B. Ram and S. Kumari [Indian J. Pure Appl. Math. 20, No. 9, 908-914 (1989; Zbl 0696.42005)] and obtain a necessary and sufficient condition for \(L^{1}\)-convergence of Fourier series under a new class \(K^\ast\) of coefficients.

MSC:

42A20	Convergence and absolute convergence of Fourier and trigonometric series
42A32	Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)

Keywords:

\(L^1\)-convergence of modified complex trigonometric sums; \(L^1\)-convergence of Fourier series; Dirichlet kernel

Citations:

Zbl 0696.42005