Determination of jumps of distributions by differentiated means |
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Authors: | R Estrada J Vindas |
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Institution: | (1) Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA |
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Abstract: | Differentiated means are defined in order to find formulas for jumps of distributions. We analyze two types of jumps occurring
in the notions of distributional jump behavior and symmetric jump behavior. We start by defining what we call Riesz differentiated
means for numerical series, then the differentiated means are extended to distributional evaluations for the Schwartz class
of tempered distributions. The jumps of tempered distributions are completely determined by the differentiated means of the
Fourier transform. We also find formulas for the jumps in terms of the asymptotic behavior of partial derivatives of harmonic
representations and harmonic conjugate functions. Applications to Fourier series are given.
The second author gratefully acknowledges support by the Louisiana State Board of Regents grant LEQSF(2005-2007)-ENH-TR-21. |
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Keywords: | and phrases" target="_blank"> and phrases primary 40C05 40C99 40H05 42A24 42A50 secondary 46F10 46F20 40A05 40D25 |
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