Fourier Serilerinin Mutlak Hausdorff Toplanabilmesi

Öz

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Anahtar Kelimeler

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FOURiER SERiLERiNiN MUTLAK HAUSDORFF TOPLANABiLMESi - ABSOLUTE HAUSDORFF SUMMABILITY OF THE FOURIER SERIES

Öz

FOURiER SERiLERiNiN MUTLAK HAUSDORFF TOPLANABiLMESi

Bu çalısmada, (μ n ) dizisi için (−p ,p ) aralığında Lebesgue anlamında integrallenebilen 2p periyotlu f fonksiyonunun Fourier serisinin n H,μ toplanabilmesi ile ilgili iki teorem ispatlanmıstır.

ABSOLUTE HAUSDORFF SUMMABILITY OF THE FOURIER SERIES

In this study, two theorems with respect to n H,μ summability of Fourier series of f
function which has 2p period and integrable in the mean of Lebesgue in the interval (−p ,p ) for sequence ( ) n μ , are proved .

Anahtar Kelimeler

• Fourier serisi, Toplanabilme, Mutlak Hausdorff toplanabilme

Kaynakça

1. Bosanquet. L.S., “Note on the Absolute summability (C) of a Fourier series”, J. London Math. +Soc., 11: 11-15 (1936).
2. Hurwitz, W.A. and Silverman, L.L.On the consistency and equivalence of certain definitions of summability, Trans. Am. Math. Soc. 18:1-20 (1917).
3. F. Hausdorff.; “Summationmethoden und Momentfolgen I.”, Math. Z., 9: 74-109 (1921).
4. Hardy. G.H., “Divergent series”, Oxford, (1949).
5. Morley, H., “A theorem on Hausdorff transformations and its applications to Cesa’ro and Hölder means”, J. London Math. Soc., 25: 168- 173 (1950).
6. Tripathy, N., “On the Absolute Hausdorff summability of Fourier series”, J. London Math. Soc., 44: 15- 25 (1969).
7. Knopp, K. and Lorentz, G.G., “Beitrage zur absoluten Limitierung”, Arch. Math., 2: 10-16 (1950).
8. Titchmarsh, E. C. ‘’Theory of Functions’’, Oxford University Pres, (1949).

9. Widder, D.V., “The Laplace Transform”, 152, Princeton, (1946).
10. Geliş Tarihi: 16/04/2011
11. Kabul Tarihi: 10/08/2011