J.-W Feng ; S Kanemitsu ; T Kuzumaki - Arithmetical Fourier transforms and Hilbert space: Restoration of the lost legacy

hrj:7426 - Hardy-Ramanujan Journal, May 6, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020 - https://doi.org/10.46298/hrj.2021.7426
Arithmetical Fourier transforms and Hilbert space: Restoration of the lost legacy

Authors: J.-W Feng ; S Kanemitsu ; T Kuzumaki

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.


Volume: Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020
Published on: May 6, 2021
Submitted on: April 30, 2021
Keywords: Möbius inversion,Hilbert space,Arithmetical Fourier Transform,Chebyshev-Markov expansion,2010 Mathematics Subject Classification. 42A16, 11A25, 01A55,[MATH]Mathematics [math]


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