Commenced in January 2007
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Paper Count: 2

conjugate dirichlet kernel Related Publications

2 L1-Convergence of Modified Trigonometric Sums

Authors: Sandeep Kaur Chouhan, Jatinderdeep Kaur, S. S. Bhatia


The existence of sine and cosine series as a Fourier series, their L1-convergence seems to be one of the difficult question in theory of convergence of trigonometric series in L1-metric norm. In the literature so far available, various authors have studied the L1-convergence of cosine and sine trigonometric series with special coefficients. In this paper, we present a modified cosine and sine sums and criterion for L1-convergence of these modified sums is obtained. Also, a necessary and sufficient condition for the L1-convergence of the cosine and sine series is deduced as corollaries.

Keywords: conjugate dirichlet kernel, Dirichlet kernel, L1-convergence, modified sums

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1 Coefficients of Some Double Trigonometric Cosine and Sine Series

Authors: Jatinderdeep Kaur


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: Fourier Series, conjugate dirichlet kernel, conjugate fejer kernel, semi-convexity

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