Arithmetical Fourier transforms and Hilbert space: Restoration of the lost legacy

Autor:	S Kanemitsu, T Kuzumaki, J.-W Feng
Přispěvatelé:	Faculty of Engineering Sciences (Kyushu Univ.)
Rok vydání:	2021
Předmět:	Pure mathematics Hilbert space 2010 Mathematics Subject Classification. 42A16 11A25 01A55 symbols.namesake Fourier transform Arithmetical Fourier Transform symbols Arithmetic function Chebyshev-Markov expansion [MATH]Mathematics [math] Mobius inversion Möbius inversion Mathematics
Zdroj:	Hardy-Ramanujan Journal Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2021, Volume 43-Special Commemorative volume in honour of Srinivasa Ramanujan, pp.56-68
ISSN:	2804-7370
DOI:	10.46298/hrj.2021.7426
Popis:	In this survey-type paper we show that the seemingly unrelated two fields-Chebyshev-Markov expansion (CME) [On83] and Arithmetical Fourier Transform (AFT) [Che10]-are indeed different looks of one entity, by the plausible missing link-Romanoff-Wintner theory (RWT). RWT generalizes both approaches, CME and AFR, and was developed in [Wi44] and [Ro51a], [Ro51b] which were written independently. These two lost researches are very closely related and effective for producing new number-theoretic identities. Cf. [CKT09] for fragmental restoration of them.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e8dee8328d33ea2fb1f92959141f3f34 https://doi.org/10.46298/hrj.2021.7426 Zobrazit plný text záznamu