Vol. 30, No. 2, 1969

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Summability of Fourier series by triangular matrix transformations

H. P. Dikshit

Vol. 30 (1969), No. 2, 399–410
Abstract

Hille and Tamarkin have proved a result for the Nörlund summability of the Fourier series of f(t) at t = x, under the hypothesis (i) φ(t) = {f(x + t) + f(xt) 2f(x)}2 = o(1),t 0, which includes as a special case the corresponding result for the Cesàro summability. However, under the lighter condition (ii) 0tφ(u)du = o(t),t 0, Astrachan has proved a theorem for the Nörlund summability which does not cover the corresponding Cesàro case. The object of the present paper is to prove theorems for the Nörlund summability and another triangular matrix method of summability which are subtler than Astrachan’s theorem in the sense that they include as a special case the corresponding result for the Cesàro summability.

Mathematical Subject Classification
Primary: 42.20
Milestones
Received: 3 May 1968
Published: 1 August 1969
Authors
H. P. Dikshit