On the summability of derived Fourier series

Logarithmic Summability of Fourier Series

A set of regular summations logarithmic methods is introduced. This set includes Riesz and Nörlund logarithmic methods as limit cases. The application to logarithmic summability of Fourier series of continuous and integrable functions are given. The kernels of these logarithmic methods for trigonometric system are estimated.

Generalized matrix summability of a conjugate derived Fourier series

The study of infinite matrices is important in the theory of summability and in approximation. In particular, Toeplitz matrices or regular matrices and almost regular matrices have been very useful in this context. In this paper, we propose to use a more general matrix method to obtain necessary and sufficient conditions to sum the conjugate derived Fourier series.

On the Summability of the Differentiated Fourier Series

On the Summability of Fourier Series. Fifth Note.

and evaluating the generalized sum of (1) as the lim rm(x; f). The matrix ?2 will be subjected to the restrictions (i-iv) below. These restrictions are of such general nature, however, that they are satisfied by a great majority of the definitions of summability known in the literature. Our first condition on 21 is significant only in the case where 91 is of infinite reference. It is automatica...

On the Restricted Cesaro Summability of Double Fourier Series

and po.biu, v), («, v), has been considered by a number of writers. Gergen and Littauer [4, Theorems IV and V] have treated the problem of the boundedness, and convergence in the Pringsheim sense, of ...