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Slice Regular Malmquist–Takenaka System in the Quaternionic Hardy Spaces

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Abstract

In this paper the slice regular analogue of the Malmquist–Takenaka system is introduced. It is proved that, under certain restrictions regarding to the parameters of the system, they form a complete orthonormal system in the quaternionic Hardy spaces of the unit ball. The properties of associated projection operator are also studied.

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References

  1. L. Adler, Quaternionic Quantum Mechanics and Quantum Fields, International Series of Monographs on Physics, Oxford University Press (1995).

    MATH  Google Scholar 

  2. D. Alpay, F. Colombo, I. Sabadini, Schur functions and their realizations in the slice hyperholomorphic setting, Integral Equations Operator Theory, 72 (2012), 253–289.

    Article  MathSciNet  MATH  Google Scholar 

  3. D. Alpay, F. Colombo and I. Sabadini, Schur Analysis in the Hyperholomorphic Setting, Springer (2016).

    Book  MATH  Google Scholar 

  4. C. Bisi and C. Stoppato, Regular vs. classical Möbius transformations of the quaternionic unit ball, in: Chapter Advances in Hypercomplex Analysis, vol. 1 of Springer INdAM Series (2013), pp. 1–13.

    Google Scholar 

  5. F. Colombo, G. Gentili, I. Sabadini, A Cauchy kernel for slice regular functions, Ann. Global Anal. Geom., 37 (2010), 361–378.

    Article  MathSciNet  MATH  Google Scholar 

  6. F. Colombo, J. O. González-Cervantes, and I. Sabadini, Some integral representations of slice hyperholomorphic functions, Moscow Math. J., 14 (2014), 473–489.

    MathSciNet  MATH  Google Scholar 

  7. F. Colombo, G. Gentili, I. Sabadini and D. Struppa, Extension results for slice regular functions of a quaternionic variable, Adv. Math., 222 (2009), 1793–1808.

    Article  MathSciNet  MATH  Google Scholar 

  8. F. Colombo, I. Sabadini and D. C. Struppa, Noncommutative Functional Calculus. Theory and Applications of Slice Hyperholomorphic Functions, Progress in Mathematics, vol. 289, Birkhäuser, Springer (Basel, 2011).

  9. C. de Fabritiis, G. Gentili and G. Sarfatti, Quaternionic Hardy Spaces, arXiv:1404.1234 (2014).

    Google Scholar 

  10. G. Gentili, C. Stoppato and D. C. Struppa, Regular Functions of a Quaternionic Variable, Springer Monographs in Mathematics, Springer (Berlin–Heidelberg, 2013).

    Book  MATH  Google Scholar 

  11. G. Gentili and D. C. Struppa, A new approach to Cullen-regular functions of a quaternionic variable, C. R. Math. Acad. Sci. Paris, 342 (2006), 741–744.

    Article  MathSciNet  MATH  Google Scholar 

  12. G. Gentili and D. C. Struppa, A new theory of regular functions of a quaternionic variable, Adv. Math., 216 (2007), 279–301.

    Article  MathSciNet  MATH  Google Scholar 

  13. F. Malmquist, Sur la détermination d’une classe functions analytiques par leurs dans un ensemble donné de points, in: Comptes Rendus Sixiéme Congrés des mathématiciens scandinaves (1925), Gjellerup (Copenhagen, 1925), pp. 253–259.

    Google Scholar 

  14. M. Pap and F. Schipp, Malmquist–Takenaka systems and equilibrium conditions, Math. Pannon., 12/2 (2001), 185–194.

    MathSciNet  MATH  Google Scholar 

  15. M. Pap, Properties of discrete rational orthogonal systems, in: Constructive Function Theory, Varna 2002 (B. Bojanov, Ed.), Dabra (Sofia, 2003), pp. 374–379.

    Google Scholar 

  16. M. Pap and F. Schipp, Malmquist–Takenaka systems over the set of quaternions, Pure Math. Appl., 15 (2004), 261–274.

    MathSciNet  MATH  Google Scholar 

  17. C. Stoppato, Regular Moebius transformations of the space of quaternions, Ann. Global Anal. Geom., 39 (2010), 387–401.

    Article  MathSciNet  MATH  Google Scholar 

  18. S. Takenaka, On the orthogonal functions and a new formula of interpolation, Japanese J. Math. II. (1925), 129–145.

    Article  MATH  Google Scholar 

  19. T. Qian, W. Sprossig and J. Wang, Adaptive Fourier decomposition of functions in quaternionic Hardy spaces, Math. Methods Appl. Sci., 35 (2012), 43–64.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Faculty of Sciences, University of Pécs, 7634, Pécs, Ifjúság út 6, Hungary

    M. Pap

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  1. M. Pap
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Correspondence to M. Pap.

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The present scientific contribution is dedicated to the 650th anniversary of the foundation of the University of Pécs, Hungary

This project has been supported by the European Union, co-financed by the European Social Fund EFOP-3.6.1.-16-2016-00004.

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Pap, M. Slice Regular Malmquist–Takenaka System in the Quaternionic Hardy Spaces. Anal Math 44, 99–114 (2018). https://doi.org/10.1007/s10476-018-0109-0

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  • DOI: https://doi.org/10.1007/s10476-018-0109-0

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