Pythagorean harmonic summability of Fourier series

This paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with the introduction of new concepts like the smoothing operator and semi-harmonic summation. The smoothing operator is demonstrated to be Kal...

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Autor principal:	Haidar Nassar H. S.
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	single fourier series linear summability smoothing operator pythagorean harmonic summability semi-harmonic summability 40g99 42a24 42a99 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/36a23e5d377f472c9e255e9d8f8eeb89
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id	oai:doaj.org-article:36a23e5d377f472c9e255e9d8f8eeb89
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spelling	oai:doaj.org-article:36a23e5d377f472c9e255e9d8f8eeb892021-12-05T14:10:45ZPythagorean harmonic summability of Fourier series2391-466110.1515/dema-2021-0025https://doaj.org/article/36a23e5d377f472c9e255e9d8f8eeb892021-07-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0025https://doaj.org/toc/2391-4661This paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with the introduction of new concepts like the smoothing operator and semi-harmonic summation. The smoothing operator is demonstrated to be Kalman filtering for linear summability, logistic processing for Pythagorean harmonic summability and linearized logistic processing for semi-harmonic summability. An emerging direct inapplicability of harmonic summability to seismic-like signals is shown to be resolvable by means of a regularizational asymptotic approach.Haidar Nassar H. S.De Gruyterarticlesingle fourier serieslinear summabilitysmoothing operatorpythagorean harmonic summabilitysemi-harmonic summability40g9942a2442a99MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 212-232 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	single fourier series linear summability smoothing operator pythagorean harmonic summability semi-harmonic summability 40g99 42a24 42a99 Mathematics QA1-939
spellingShingle	single fourier series linear summability smoothing operator pythagorean harmonic summability semi-harmonic summability 40g99 42a24 42a99 Mathematics QA1-939 Haidar Nassar H. S. Pythagorean harmonic summability of Fourier series
description	This paper explores the possibility for summing Fourier series nonlinearly via the Pythagorean harmonic mean. It reports on new results for this summability with the introduction of new concepts like the smoothing operator and semi-harmonic summation. The smoothing operator is demonstrated to be Kalman filtering for linear summability, logistic processing for Pythagorean harmonic summability and linearized logistic processing for semi-harmonic summability. An emerging direct inapplicability of harmonic summability to seismic-like signals is shown to be resolvable by means of a regularizational asymptotic approach.
format	article
author	Haidar Nassar H. S.
author_facet	Haidar Nassar H. S.
author_sort	Haidar Nassar H. S.
title	Pythagorean harmonic summability of Fourier series
title_short	Pythagorean harmonic summability of Fourier series
title_full	Pythagorean harmonic summability of Fourier series
title_fullStr	Pythagorean harmonic summability of Fourier series
title_full_unstemmed	Pythagorean harmonic summability of Fourier series
title_sort	pythagorean harmonic summability of fourier series
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/36a23e5d377f472c9e255e9d8f8eeb89
work_keys_str_mv	AT haidarnassarhs pythagoreanharmonicsummabilityoffourierseries
_version_	1718371760088285184

Pythagorean harmonic summability of Fourier series

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