Distributional Point Values and Convergence of Fourier Series and Integrals |
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Authors: | Jasson Vindas Ricardo Estrada |
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Institution: | (1) Mathematics Department, Louisiana State University, Baton Rouge, Louisiana, USA |
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Abstract: | In this article we show that the distributional point values of a tempered distribution are characterized by their Fourier
transforms in the following way: If
and
, and
is locally integrable, then
distributionally if and only if there exists k such that
, for each a > 0, and similarly in the case when
is a general distribution. Here
means in the Cesaro sense. This result generalizes the characterization of Fourier series of distributions with a distributional
point value given in 5] by
. We also show that under some extra conditions, as if the sequence
belongs to the space
for some
and the tails satisfy the estimate
,\ as
, the asymmetric partial sums\ converge to
. We give convergence results in other cases and we also consider the convergence of the asymmetric partial integrals. We
apply these results to lacunary Fourier series of distributions. |
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Keywords: | |
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