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Coefficients of Some Double Trigonometric Cosine and Sine Series

Authors: Jatinderdeep Kaur

Abstract:

In this paper, the results of Kano from one dimensional cosine and sine series are extended to two dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as class of semi convexity and class R are extended from one dimension to two dimensions. Further, the function f(x, y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function or not, has been studied. Moreover, some results are obtained which are generalization of Moricz’s results.

Keywords: Conjugate Dirichlet kernel, conjugate Fejer kernel, Fourier series, Semi-convexity.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1338496

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References:


[1] A. Zygmund, Trigonometric Series, Vol. I & Vol. II, Cambridge Univ. Press, 1959.
[2] F. M´oricz, Convergence and integrability of double trigonometric series with coefficients of bounded variation, Proc. Amer. Math. Soc., 3(1988), 633-640.
[3] F. M´oricz, Integrability of double trigonometric series with special coefficients, Anal. Math., 16(1990), 39-56.
[4] F. M´oricz, On double cosine, sine and Walsh series with monotone coefficients, Proc. Amer. Math. Soc., 109(2) (1990), 417-425.
[5] F. M´oricz, On the integrability and L1-convergence of double trigonometric series, Studia Math., 98 (3) (1991), 203-225.
[6] J. Kaur and S.S. Bhatia, The Extension of the Theorem of J. W. Garrett C. S. Rees and C. V. Stanojevic from One Dimension to Two Dimension, International Journal of Mathematics Analysis, Vol. 3(26) (2009), 1251 - 1257.
[7] J. Kaur and S.S. Bhatia, Integrability and L1- Convergence of Double Trigonometric Series, Analysis in Theory and Applications, vol. 27 (1)(2011), 32-39.
[8] K. Kaur, S.S. Bhatia and B. Ram, Double trigonometric series with coefficients of bounded variation of higher order, Tamkang J. Math., 35(4)(2004), 267-280.
[9] N.K. Bary, A treatise on trigonometric series, Vol I and Vol II, Pergamon Press, London (1964).
[10] C.P. Chen and Y.W. Chauang, L1-convergence of double Fourier series, Chinese J. Math., 19 (4)(1991), 391-410.
[11] S.A. Teljakovskˇii, Some estimates for trigonometric series with quasi-convex coefficients, Mat. Sb., 63(105)(1964), 426-444.
[12] T. Kano, Coefficients of some trigonometric series, J. Fac. Sci. Shinshu Univ., 3(1968), 153-162.