ON THE DOUBLE NORLUND SUMMABILITY OF DOUBLE FOURIER SERIES

Article Sidebar

PDF
Published: Jun 1, 1996
DOI: https://doi.org/10.5556/j.tkjm.27.1996.4351
Keywords:
Double Fourier series double Norlund summability

Main Article Content

YASUO OKUYAMA
Department of Mathematics, Faculty of Engineering, Shinshu University, Nagano 380, Japan
IKUKO MIYAMOTO
Department of Mathematics and Informatics, Faculty of Science, Chiba University, Chiba 263, Japan.

Abstract




We extend Rajagopal's theorem [12] to a theorem on the dou­ ble Norlund summability of double Fourier series, from which various known results are deduced.




Article Details

How to Cite
OKUYAMA, Y., & MIYAMOTO, I. (1996). ON THE DOUBLE NORLUND SUMMABILITY OF DOUBLE FOURIER SERIES. Tamkang Journal of Mathematics, 27(2), 133–144. https://doi.org/10.5556/j.tkjm.27.1996.4351
Issue
Vol. 27 No. 2 (1996)
Section
Papers
Creative Commons License

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

References

Y. S. Chow, "On the Cesaro summability of double Fourier series," Tohoku Math. J., 5(1953), 277-283.

J. J. Gergen, "Convergence criteria for double Fourier series," Trans. Amer. Math. Soc., 35(1933), 29-63.

G. H. Hardy, "On the summability of Fouier series," Proc. London Math. Soc., 12(1913), 365-372.

J. G. Herriot, "The Norlund summability of double Fouier series," Trans. Amer. Math. Soc., 59(1942), 72-94.

E. Hille and J. D. Tamarkin, "On the summability of Fouier series," Trans. Amer. Math. Soc., 34(1932), 757-783.

H. Hirokawa,"On the Norlund summability of Fouier series and its conjugate series," Proc. Japan Acad., 44(1968), 449-451.

H. Hirokawa and I. Kayashima, " On a sequence of Fourier coefficients," Proc. Japan Acad., 50(1974), 57-62.

E. W. Hobson, Theory of functions of a real variable, Cambridge, Vol.l, 1927

L. McFadden, "Absolute Norlund summability," Duke Math. J., 9(1942), 168-207

K. N. Mishra, "Summability of double Fourier series by double Norlund method," Bull. Inst. Math. Acad. Sinica., 13(1985), 289-295

T. Pati, "A generalization of a theorem of lgengar on the harmonic summability of Fourier series," Indian J. Math., 3(1961), 85-90.

C. T . Rajagopal, "On the Norlund summability of Fourier series," Proc. Camb. Phil. Soc., 59(1963), 47-53.

P. L. Sharma, "On the harmonic summability of double Fouier series," Proc. Amer. Math. Soc., 91(1958), 979-986.

J. A. Siddiqi, "On the harmonic summability ofFouier series," Proc. Nat. Acad. Sci. India Sect.A., 28(1948), 527-531.

T. Singh, "On Norlund summability of Fouier series and its conjugate series," Proc. Nat. Inst. Sci India Part A., 29(1963), 65-73.

T. Singh,"Norlund summability of Fourier series and its conjugate series," Ann. Mat. Pura Appl., 64(1964), 123-132.