In this work, the theory of L¹-convergence for some classes of trigonometric series is elaborated. The work contains four chapters in which some new results are obtained. Also, new proofs of some well known theorems are given. A classical result concerning the integrability and L¹-convergence of a cosine series
(C)
with convex coefficients is the well known theorem of Young. Later, Kolmogorov extended Young’s result for series (C) with quasi-convex coefficients and also showed that such cosine...
Mathematics Subject Classification: Primary 33E20, 44A10; Secondary 33C10, 33C20, 44A20
By using integral representations for several Mathieu type series, a number
of integral transforms of Hankel type are derived here for general families
of Mathieu type series. These results generalize the corresponding ones on
the Fourier transforms of Mathieu type series, obtained recently by Elezovic
et al. [4], Tomovski [19] and Tomovski and Vu Kim Tuan [20].
Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12,
33E20, 40A30
The main purpose of this paper is to present a number of potentially
useful integral representations for the generalized Mathieu series as well as
for its alternating versions via Mittag-Leffler type functions.
Download Results (CSV)