On the absolute summability of factored Fourier series

Summary In this paper the author has considered the harmonic summability of the factored Fourier series when ϕα(t), α > 0, is of bounded variation.     

On the absolute Riesz summability of orthogonal series

- , [4]. , .     

Matrix summability of a factored Fourier series

This paper reports a result for proving a triangular matrix summability of a factored Fourier series by extending the theorem on Nörlund summability of a factored Fourier series att =x when ?(t)∈B.V in (0, π) due to Singh [4] (Indian J. Math. 9 227–236). The result generalizes the theorem of Varshney [5] (Proc. Am. Math. Soc. 10, 784–789) and that of Singh.     

Some new results on absolute Riesz summability of infinite series and Fourier series

In this paper, some known results on the absolute Riesz summability factors of infinite series and Fourier series have been proved under weaker conditions. Some new and known results are also obtained.     

On the newly generalized absolute Riesz summability of orthogonal series

[3] , [1], ¦C,,(t)¦ _k - . , , ¦R, , (t)¦ _k - ¦R, , (t)¦ _k - . (t)=1,k=1 [7], [9].

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This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant#T 016 393.     

Absolute matrix summability of a factored Fourier series

A theorem for a factored Fourier series is proved.     

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.     

On the absolute summability of Fourier series of almost-periodic besicovitch functions

For almost-periodic Besicovitch functions whose spectrum has a limit point only at infinity, we establish criteria for the absolute Cesàro summability of their Fourier series of order greater than –1.     

Generalized absolute Cesaro summability of a Fourier series

In an attempt to study the scope of a theorem due to Pati, the authors have established that φ(t) logK|t∈B _u V in (0,π)⟹ΣA _n (x) is |C, 0,β| forβ>1, at the pointt = x.     

On the absolute summability of trigonometric series

{_n} a _{n n} , s _n n- , _n -n- (, 1)- . . . -, . , «|s₂n+1–s ₂ n¦< . .» «¦ _n – _n–1¦< . .» . s. , {a _n } 0, a _n/n<, {a _n } , {it|_n¦<. , , -.     

On the local properties of factored Fourier series

Quite recently, Bor [H. Bor, On the local properties of factored of Fourier series, Bull. Math. Anal. Appl. 1 (2009) 15-21] proved a theorem on the local property of summability of factored Fourier series. The purpose of this paper is to extend to more general cases by taking normal matrices in place of weighted mean matrices.