On the Convergence of a Factored Fourier Series and its Allied Series

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Authors

  • M. K. Nayak

Abstract

In § 2 we prove a number of necessary lemmas for the purpose. In § 3 we prove the following Theorems 1 and 2. In § 4 we develop convergence Theorems 3 and 4 of factored Fourier series and its allied series.

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Published

1972-12-01

How to Cite

Nayak, M. K. (1972). On the Convergence of a Factored Fourier Series and its Allied Series. The Journal of the Indian Mathematical Society, 36(3-4), 215–227. Retrieved from https://informaticsjournals.co.in/index.php/jims/article/view/16665

Issue

Volume 36, Issue 3-4, September-December 1972

Section

Articles

License

Copyright (c) 1972 M. K. Nayak

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

G. H. HARDY: The summability of a Fourier series by logarithmic means, Quart. J. Math. Oxford, Ser. 2(1931), 107-72.

G. H. HABDY and M. RIESZ: The general theory of Dirichlet's series, Cambridge (1915).

L. S. BOSANQUET and J. M. HYSLOP: On the absolute summability of the allied series of a Fourier series, Math. Zeitschrift, 42 (1937), 489-512.

L. S. BOSANQUET and A. C. OFFOBD: Note on Fourier series, Composito Math., 1 (1935), 180-187.

R. MoHANTY: On the convergence factor of a Fourier series, Proc. Cambridge Phil. Soc., 63 (1967), 129-131.

R. MQHANTY and B. K. RAY: On the convergence factor of a Fourier series, Proc. Cambridge Phil. Soc, 65 (1969), 75-85.

R. MOHANTY and B. K. RAY : On the behaviour of a series associated with the conjugate series of a Fourier series, Canadian J. of Math., Vol. XXI. No. 3, (1969), 535-551.

R. MOHANTY and MANMADHA J. RAO: On some sequences connected with Fourier series. J.I.M.S., Vol. XXXII (1968), 7-15.

M. L. MISBA: On the summability of the conjugate series of a Fourier series by logarithmic means, Proc. Nat. Inst. Sci. India, 13 (1947), 157-168; also see Math. Review, Vol. 10 (1949), 247-48.