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On the absolute Nörlund summability factors of a Fourier series and its conjugate series at a point

  • Kôsi Kanno (a1)
Abstract

The object of this paper is to give generalizations of Okuyama's Theorem [Bull. Austral. Math. Soc.12 (1975), 9–21, Tôohoku Math. J. (2) 28 (1976), 563–581] on the absolute Nörlund summability factors of a Fourier series and its conjugate series.

Our theorems imply many results proved by other authors: especially Theorem 1 includes the results of Bhatt and Kishor [Indian J. Math.9 (1967), 259–267 (1968)], Dikshit [Pacific J. Math.63 (1976), 371–379], and Lal [Publ. Inst. Math. (Beograd) 20 (34) (1976), 169–178], and we can easily deduce Lal's result [Indian J. Math.16 (1974), 1–22] from our Corollary 2.

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Copyright
COPYRIGHT: © Australian Mathematical Society 1979
References
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[1]Bhatt, Shri Nivas and Kishore, Nand, “Absolute Nörlund summability of a Fourier series”, Indian J. Math. 9 (1967), 259–267 (1968).
[2]Dikshit, G.D., “Absolute Nörlund summability factors for Fourier series”, Pacific J. Math. 63 (1976), 371–379.
[3]Kanno, Kôsi and Watanabe, Satoshi, “On the absolute summability of factored Fourier series”, Bull. Yamagata Univ. Natur. Sci. 9 (1977), 197–203.
[4]Kishore, Nand, “Absolute Nörlund summability of a factored Fourier series”, Indian J. Math. 9 (1967), 123–136.
[5]Lal, Shiva Narain, “On the absolute Nörlund summability factors of a Fourier series”, Indian J. Math. 16 (1974), 1–22.
[6]Lal, Shiva Narain, “On the absolute Nörlund summability of a series associated with a Fourier series”, Publ. Inst. Math. (Beograd) 20 (34) 1976, 169–178.
[7]Matsumoto, Kishi, “On absolute Cesàro summability of a series related to a Fourier series”, Tôhoku Math. J. (2) 8 (1956), 205–222.
[8]Mehrotra, Narain Das, “On the absolute Nörlund summability of a factored Fourier series”, Proc. Japan. Acad. 41 (1965), 46–51.
[9]Mohapatra, R.N., Das, G. and Srivastava, V.P., “On absolute summability factors of infinite series and their application to Fourier series”, Proc. Cambridge Philos. Soc. 63 (1967), 107–118.
[10]Okuyama, Yasuo, “On the absolute Nörlund summability factors of Fourier series”, Bull. Austral. Math. Soc. 12 (1975), 9–21.
[11]Okuyama, Yasuo, “On the absolute Nörlund summability factors of the conjugate series of a Fourier series”, Tôhoku Math. J. (2) 28 (1976), 563–581
[12]Prasad, B.N. and Bhatt, S.N., “The summability factors of a Fourier series”, Duke Math. J. 24 (1957), 103–117.
[13]Varshney, O.P., “On the absolute harmonic summability of a series related to a Fourier series”, Proc. Amer. Math. Soc. 10 (1959), 784–789.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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