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On the absolute summability of the allied integral by a functional Nörlund method


Author: Shiva Narain Lal
Journal: Proc. Amer. Math. Soc. 42 (1974), 113-120
MSC: Primary 42A28; Secondary 40G05
DOI: https://doi.org/10.1090/S0002-9939-1974-0324295-2
MathSciNet review: 0324295
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Abstract: In this paper a theorem on the absolute summability of an integral associated with the allied integral of a Fourier integral by a functional Nörlund method has been established. Our theorem generalises an earlier result due to Boĭcun on the absolute Nörlund summability of the allied integral.


References [Enhancements On Off] (What's this?)

  • [1] L. G. Boĭcun, Absolute summability of conjugate Fourier integrals by the method of G. F. Voronoĭ, Izv. Vysš. Učebn. Zaved. Matematika 1967 (1967), no. 6 (61), 11–21 (Russian). MR 0221202
  • [2] Leonard McFadden, Absolute Nörlund summability, Duke Math. J. 9 (1942), 168–207. MR 0006379
  • [3] E. C. Titchmarsh, Introduction to the theory of Fourier integrals, Clarendon Press, Oxford, 1937.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0324295-2
Keywords: Allied integral, absolutely $ (N,p(y))$ summable, Cesàro's method $ \vert C,\alpha \vert$
Article copyright: © Copyright 1974 American Mathematical Society

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