Extension of inverse q-Fourier transform via conformal mapping

Gilberto M. Nakamura, Alexandre H. de Martini and Alexandre S. Martinez

Physica A: Statistical Mechanics and its Applications, 2019, vol. 524, issue C, 106-111

Abstract: We extend the generalized q-Fourier transform to include arbitrary values of the non-extensive parameter q. The procedure involves conformal mapping and provides the inverse q-Fourier transform if the extended q-Fourier exists. In addition, the extended q-Fourier transform preserves linearity and it q-generalizes translation symmetry. As an application, we argue the q parameter can be extracted from log-periodic signals.

Keywords: Nonextensive statistical mechanics; q-Fourier transform; Box–cox data transformation; Complex systems; Log-periodicity (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:524:y:2019:i:c:p:106-111

DOI: 10.1016/j.physa.2019.03.016

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