Differentiation of Fourier Series via Orthogonal Derivative

It is very known that if the operator d/dx acts on each term into a convergent Fourier Series (FS), then it may result a divergent series. This situation is remedied applying the symmetric derivative to FS, which implies the existence of the important Fejér-Lanczos Factors. In this paper, we show that the orthogonal derivative also leads to these Factors.Journal of Institute of Science and Technology, 2015, 20(2): 113-114

Operator ideals and the absolute convergence of Fourier series

In this paper we give some relationships between the absolutely convergent Fourier series of functions belonging to Besov spaces and their connection with the theory of operator ideals. In this context, we give results in operator ideals associated with generalized approximation numbers, Weyl numbers and entropy numbers.