A nice asymptotic reproducing kernel

Raymond Mortini

doi:10.56754/0719-0646.2503.441

DOI:

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

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.

Keywords

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

Mathematics Subject Classification:

26A99 , 47B34

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

Pages: 441–446
Date Published: 2023-12-22
Vol. 25 No. 3 (2023)

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

Y. Katznelson, An introduction to harmonic analysis. New York, USA: Dover Publications, Inc., 1976.

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.