Pythagorean harmonic summability of Fourier series

• Autorzy: Haidar Nassar H. S.

Identyfikatory

DOI

10.1515/dema-2021-0025

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

single Fourier series; linear summability; smoothing operator; Pythagorean harmonic summability; semi-harmonic summability

PL

szereg Fouriera; sumowalność szeregu; twierdzenie Pitagorasa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2021
• Tom: Vol. 54, nr 1
• Strony: 212--232
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Haidar Nassar H. S.

• Euclidean Press LLC, 77 Ibrahim Abdul Al Str., Hamra, Beirut, Lebanon

• https://orcid.org/0000-0002-7568-0835

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Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).