Matrix Summability Of Fourier Series Research Articles

A new theorem on absolute matrix summability of fourier series

We generalize a main theorem dealing with absolute weighted mean summability of Fourier series to the |A,pn|k summability factors of Fourier series under weaker conditions. Also some new and known results are obtained.

On the absolute matrix summability of Fourier series and some associated series

The object of the paper is to study the absolute matrix summability problem of Fourier series, conjugate series and some associated series under a new set of conditions on matrix methods, generalising many known results in the literature.

Absolute Nörlund matrix summability of Fourier series based on inclusion theorems

In a recent paper [39] the second author established sufficient conditions for a Nörlund matrix (N, p) to be stronger than a Cesaro matrix (C, α) of order α, for some positive α. This result was then used to show that a number of known theorems dealing with the Nörlund summability of Fourier series, or related series, can be more easily established, since the conditions placed on the Nörlund matrix imply that it is stronger than some (C, α) method, for which the summability theorem has already been established.

Matrix summability of Fourier series based on inclusion theorems, II

On utilise des theoremes d'inclusion pour demontrer la sommabilite matricielle de series de Fourier

Matrix summability of Fourier series based on inclusion theorems

Letdenote the Fourier series expansion of a function. Féver's celebrated theorem states that the series is summable (C, 1) at each point of continuity off, where (C, 1) denotes the Cesàro method of summability of order 1. Riesz extended this result to (C, α) for each α > 0. Since then many authors have established sufficient conditions on various methods of summability to guarantee similar results. Over the years the pattern has been to strive for weaker conditions on the matrix, and to replace the condition of continuity on the function by a less stringent one. Theorems have been proved not only for the summability off, but the summability of the derived series, and other series, related tof. Beginning with the work of Hille and Tamarkin[13], many of the theorems have been extended to absolute summability.

Matrix summability of Fourier series

Matrix summability of Fourier series

On the absolute matrix summability of Fourier series

On the absolute matrix summability of Fourier series