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Asymptotic behavior of the dirichlet kernel of fourier sums with respect to a polygon

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Abstract

One investigates the behavior for R→+∞ of the two-dimensional Dirichlet kernels

, where W⊂ℝ2 is a fixed polygon. It is known that

for any polygon, and

, if the coordinates of all the vertices of W are rational numbers. It is shown that in the general case the second result is not true: there exists a triangle W such that

.

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Literature cited

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Authors
  1. A. N. Podkorytov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 149, pp. 142–149, 1986.

The author is grateful to G. I. Natanson and V. P. Khavin for useful discussion.

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Podkorytov, A.N. Asymptotic behavior of the dirichlet kernel of fourier sums with respect to a polygon. J Math Sci 42, 1640–1646 (1988). https://doi.org/10.1007/BF01665052

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  • DOI: https://doi.org/10.1007/BF01665052

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