On the relation between Riemann and Abel summability of trigonometrical series

Summary Szász established a relation between summability (R, 1) andCesàro summability of positive order. These results were generalised byYano who also established the corresponding Result for summability (R', 1). Generalising the result ofYano, here we shall determine the relation between summability (R', p) andAbel summability of trigonometrical series for all finite integral values of p>-1.     

级数的常规可和，Cesàro可和与Abel可和的几点讨论

讨论级数常规可和、Cesaro可和与Abel可和的关系．利用数学分析级数理论,证明Abel可和适用范围最广,Cesaro可和其次,级数常规可和适用范围最小．这个结论丰富了经典级数理论,为实际应用中选用合适可和提供依据．     

Absolute summability of infinite series

It is shown in [4] that if a normal matrix,A satisfies some conditions then |C,1| _k summability implies |A| _k summability wherek≥1. In the present paper, we consider the converse implication.     

Convergence and summability of Fourier series

In this note we study (C, –) summability, 0<1, of Fourier series and their conjugates in the sense of convergence with respect to the L^P norm, 1p+.Translated from Matematicheskie Zametki, Vol. 19, No. 6, pp. 887–898, June, 1976.     

Points of strong summability of fourier series

We study strong means of deviations of partial sums of expansions of functionsf in systems of functions of polynomial type.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 12, pp. 1655–1664, December, 1994.     

Points of strong summability of Fourier series

The points of a function f L at which there are given estimates of the rate of convergence to zero of the strong arithmetic means of its Fourier series and the trigonometrically conjugate series are characterized.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 8, pp. 1020–1031, August, 1992.     

Points of strong summability of Fourier series

In this paper we present a new solution of Hardy and Littlewood's problem concerning strong summability of Fourier series; we also present a property of points of strong summability.Translated from Matematicheskie Zametki, Vol. 14, No. 5, pp. 615–626, November, 1973.     

On convergence and summability of Fourier series

. , , –1<<0. .

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The present work was written on the basis of two earlier works received byAnalysis Mathematica on January 16, 1979, and July 20, 1979.