Title: AN ESTIMATE OF THE RATE OF CONVERGENCE OF CESARO MEANS OF FOURIER SERIES OF FUNCTIONS OF BOUNDED VARIATION
Abstract: This chapter presents an estimate of the rate of convergence of Cesaro means of Fourier series of functions of bounded variation. It discusses a periodic function with period 2π and Lebesgue integrable on [−π, π]. It is assumed that ½ a 0 + ∑( a k cos kx + b k sin kx ) is the Fourier series of f . S n ( f , x ) denotes the partial sums of the Fourier series of f such that S n ( f , x ) = ½ a 0 + ∑( a k cos kx + b k sin kx ). It is known that if f is a function of bounded variation on [−π, π], then lim ( s n ( f , x ) − ½ ( f ( x + 0) + f ( x −0))) = 0. The chapter discusses a sharper version of this result. It presents a generalization of this sharper version of the result in a slightly different direction. The chapter presents the summability method for Fourier series of functions of bounded variation on [−π, π].
Publication Year: 1988
Publication Date: 1988-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 7
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