IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v524y2019icp106-111.html
   My bibliography  Save this article

Extension of inverse q-Fourier transform via conformal mapping

Author

Listed:
  • Nakamura, Gilberto M.
  • de Martini, Alexandre H.
  • Martinez, Alexandre S.

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.

Suggested Citation

  • Nakamura, Gilberto M. & de Martini, Alexandre H. & Martinez, Alexandre S., 2019. "Extension of inverse q-Fourier transform via conformal mapping," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 106-111.
    • Handle: RePEc:eee:phsmap:v:524:y:2019:i:c:p:106-111
    DOI: 10.1016/j.physa.2019.03.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119302353
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.03.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Plastino, A. & Rocca, M.C., 2012. "Inversion of Umarov–Tsallis–Steinberg’s q-Fourier transform and the complex-plane generalization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4740-4747.
    2. Kalogeropoulos, Nikos, 2012. "Distributivity and deformation of the reals from Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1120-1127.
    3. Borges, Ernesto P., 2004. "A possible deformed algebra and calculus inspired in nonextensive thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 95-101.
    4. Scarfone, A.M., 2017. "κ-deformed Fourier transform," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 480(C), pages 63-78.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Nelson, Kenric P., 2015. "A definition of the coupled-product for multivariate coupled-exponentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 187-192.
    2. Kin Keung Lai & Shashi Kant Mishra & Ravina Sharma & Manjari Sharma & Bhagwat Ram, 2023. "A Modified q-BFGS Algorithm for Unconstrained Optimization," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    3. Megías, E. & Timóteo, V.S. & Gammal, A. & Deppman, A., 2022. "Bose–Einstein condensation and non-extensive statistics for finite systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    4. Martinez, Alexandre Souto & González, Rodrigo Silva & Terçariol, César Augusto Sangaletti, 2008. "Continuous growth models in terms of generalized logarithm and exponential functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5679-5687.
    5. Marco A. S. Trindade & Sergio Floquet & Lourival M. S. Filho, 2018. "Portfolio Theory, Information Theory and Tsallis Statistics," Papers 1811.07237, arXiv.org, revised Oct 2019.
    6. Oikonomou, Th., 2007. "Tsallis, Rényi and nonextensive Gaussian entropy derived from the respective multinomial coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 119-134.
    7. Goulart, A.G. & Lazo, M.J. & Suarez, J.M.S., 2020. "A deformed derivative model for turbulent diffusion of contaminants in the atmosphere," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    8. Oikonomou, Thomas & Tirnakli, Ugur, 2009. "Generalized entropic structures and non-generality of Jaynes’ Formalism," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3027-3034.
    9. Duarte Queirós, Sílvio M., 2012. "On generalisations of the log-Normal distribution by means of a new product definition in the Kapteyn process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(13), pages 3594-3606.
    10. Balankin, Alexander S. & Mena, Baltasar, 2023. "Vector differential operators in a fractional dimensional space, on fractals, and in fractal continua," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    11. Silva, Luiz Eduardo Virgilio & Cabella, Brenno Caetano Troca & Neves, Ubiraci Pereira da Costa & Murta Junior, Luiz Otavio, 2015. "Multiscale entropy-based methods for heart rate variability complexity analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 422(C), pages 143-152.
    12. Gomez, Ignacio S. & Portesi, Mariela & Borges, Ernesto P., 2020. "Universality classes for the Fisher metric derived from relative group entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    13. Pourali, B. & Lari, B. & Hassanabadi, H., 2021. "An oscillator with position-dependent mass exposed to a thermal bosonic bath," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).
    14. Rosa, Wanderson & Weberszpil, José, 2018. "Dual conformable derivative: Definition, simple properties and perspectives for applications," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 137-141.
    15. da Silva, Sérgio Luiz Eduardo Ferreira, 2021. "Newton’s cooling law in generalised statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    16. Nelson, Kenric P. & Umarov, Sabir R. & Kon, Mark A., 2017. "On the average uncertainty for systems with nonlinear coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 30-43.
    17. Suyari, Hiroki & Wada, Tatsuaki, 2008. "Multiplicative duality, q-triplet and (μ,ν,q)-relation derived from the one-to-one correspondence between the (μ,ν)-multinomial coefficient and Tsallis entropy Sq," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 71-83.
    18. Nelson, Kenric P. & Kon, Mark A. & Umarov, Sabir R., 2019. "Use of the geometric mean as a statistic for the scale of the coupled Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 248-257.
    19. Miguel A Ré & Rajeev K Azad, 2014. "Generalization of Entropy Based Divergence Measures for Symbolic Sequence Analysis," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-11, April.
    20. Trindade, Marco A.S. & Floquet, Sergio & Filho, Lourival M. Silva, 2020. "Portfolio theory, information theory and Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:524:y:2019:i:c:p:106-111. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.