FOURIER SERİLERİNİN EŞLENİK SERİLERİNİN MUTLAK GENELLEŞTİRİLMİŞ NÖRLUND TOPLANABİLMESİ ÜZERİNE - ON ABSOLUTE GENERALIZED NORLUND SUMMABILITY OF THE CONJUGATE SERIES OF FOURIER SERIES

Yıl 2013, Cilt: 9 Sayı: 2, 25 - 30, 06.01.2015

Abdullah Sönmezoğlu

Öz

FOURIER SERİLERİNİN EŞLENİK SERİLERİNİN MUTLAK GENELLEŞTİRİLMİŞ NÖRLUND TOPLANABİLMESİ ÜZERİNE

Bu çalışmada, olmak üzere  ve  pozitif dizileri için  aralığında Lebesgue anlamında integrallenebilen  periyotlu periyodik  fonksiyonunun Fourier serisinin eşlenik serisinin   toplanabilmesi hakkında bir teorem ispatlanmıştır.

ON ABSOLUTE GENERALIZED NORLUND SUMMABILITY OF THE CONJUGATE SERIES OF FOURIER SERIES

 

In this paper , a theorem about k n n N, p ,q summability of the conjugate series of Fourier series of periodic f function which has 2π period and integrable in the mean of Lebesgue in the interval (−π ,π ) for positive sequences ( ) n p and ( ) n q , is proved where k ≥ 2 .

 

 

Anahtar Kelimeler

Yakınsaklık, Fourier serileri, Eşlenik seriler, Mutlak genelleştirilmiş Nörlund

Kaynakça

• 1. Nörlund. N.E.; Sur une application des fonctions permutables. Lunds Universitets Arsskrift 16, (1919).
• 2. Mcfadden, L., Absolute Nörlund summability.Duke Math.J , 9, 168-207,(1942).
• 3. Hardy. G.H. ;Divergent series , Oxford, (1949).
• 4 Pati, T., On the absolute Nörlund summability of a Fourier series. London Math. Soc, 34, 153-160, (1959).
• 5 Pati, T., Addendum: On the absolute Nörlund summability of a Fourier series. J.London Math. Soc, 37, 256, (1962).
• 6. Pati, T., On the absolute summability of the Conjugate series of a Fourier series by Nörlund means. J. London Math. Soc(2), 38, 204-214, (1963).
• 7. Dikshit, H. P., On the absolute of a Fourier series at a point. Proc. Cambridge Philos Soc, 65, 495-505, (1969).
• 8. Dikshit, H. P., Absolute summability of the Conjugate series of a Fourier series by Nörlund means. Math. Ann, 184, 106-112, (1970).
• 9. Pati, T., On the absolute summability of a Fourier series by Nörlund means. Math.Z, 88,244-249, (1965).
• 10. Rhoades,B. E;Savaş Ekrem.; On absolute Nörlund summability of Fourier series.Tamkang J.Math.33(4), 359-364-, (2002).
• 11.J.R.Nurcombe.; Limitation and ineffectivens theorems for absolute and strong generalised Nörlund summability.Analysis, 9, 357-365, (1989).
• 12. E. C. Titchmarsh.; Theory of Functions., Oxford University Pres, (1949).