Vol. 26, No. 2, 1968

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Nörlund summability of Fourier series

Masako Izumi and Shin-ichi Izumi

Vol. 26 (1968), No. 2, 289–301

The Nörlund summability was first applied to the theory of Fourier series by E. Hille and J. D. Tamarkin. Many other mathematicians have since worked in this field. Recently T. Singh has proved a nice theorem conceming the Nörlund summability of Fourier series. In Part I, we shall give a generalization.

Absolute Nörlund summability was defined by L. McFadden and he proved a theorem concerning the absolute Nörlund summability of the Fourier series of functions of the Lipschitz class which was generalized by S. N. Lal. We shall give another generalization of McFadden’s theorem in Part II.

Mathematical Subject Classification
Primary: 42.20
Received: 12 September 1966
Published: 1 August 1968
Masako Izumi
Shin-ichi Izumi