A nice asymptotic reproducing kernel

Raymond Mortini

doi:10.56754/0719-0646.2503.441

Authors

Raymond Mortini Université de Lorraine, Département de Mathématiques et Institut Élie Cartan de Lorraine, CNRS, F-57000 Metz, France. Current address: Université du Luxembourg, Département de Mathématiques, L-4364 Esch-sur-Alzette, Luxembourg. https://orcid.org/0000-0002-7923-1877

DOI:

https://doi.org/10.56754/0719-0646.2503.441

Keywords:

Integral kernel, reproducing kernel, good kernel, summability kernel, real analysis

Abstract

We extend the assertion of Problem 12340 in Amer. Math. Monthly 129 (2022), 686, by deriving some additional asymptotic behaviour of that special kernel.

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References

A. Garcia, “Problem 12340”, Amer. Math. Monthly, vol. 129, no. 7, p. 686, 2022, doi: 10.1080/00029890.2022.2075672.

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E. M. Stein and R. Shakarchi, Fourier analysis, ser. Princeton Lectures in Analysis. New York, USA: Princeton University Press, Princeton, 2003, vol. 1.

Z. Wang, “Studies on several kernels in Fourier analysis”, Pure Appl. Math., vol. 31, no. 3, pp. 238–244, 2015, doi: 10.3969/j.issn.1008-5513.2015.03.003.