Coefficients of Some Double Trigonometric Cosine and Sine Series

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.

Authors:

• Jatinderdeep Kaur

Keywords:

• Conjugate Dirichlet kernel
• conjugate Fejer kernel
• Fourier series
• Semi-convexity.

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