Extension of inverse q-Fourier transform via conformal mapping

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...

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Bibliographic Details
Published in:	Physica A Vol. 524; pp. 106 - 111
Main Authors:	Nakamura, Gilberto M., de Martini, Alexandre H., Martinez, Alexandre S.
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 15-06-2019
Subjects:	[formula omitted]-Fourier transform Box–cox data transformation Complex systems Log-periodicity Nonextensive statistical mechanics Log-periodicity Box–cox data transformation Nonextensive statistical mechanics Complex systems q-Fourier transform
Online Access:	Get full text
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Summary:	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. •Linear and invertible q-Fourier transform.•Generalized q-periods.•Dirac delta function.
ISSN:	0378-4371 1873-2119
DOI:	10.1016/j.physa.2019.03.016