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On the complex twisted Laplacian on \( \mathbb {C}^n\) and Poisson transform for the Heisenberg group

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Abstract

We compute the point spectrum of the complex twisted Laplacian. We also refine a Theorem proved by Thangavelu.

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References

  1. N. Askour, A. Intissar and Z. Mouayn, Explicit formulae for reproducing kernels of generalized Bargmann spaces on \({\mathbb{C} }n\), J.Math. Phys.41 (2000), 3057-3067.

    Article  MathSciNet  MATH  Google Scholar 

  2. A. Dasgupta and M.W. Wong, Essential self-adjointness and global hypoellipticity of the twisted Laplacian. Rend Sem Mat Univ Pol Torino. 2008, 66, 75-85.

    MathSciNet  MATH  Google Scholar 

  3. M. De Gosson, Spectral properties of a class of generalized Landau operators, Comm. Partial Differential Equations 33 (2008), 2096-2104.

    Article  MathSciNet  MATH  Google Scholar 

  4. X. Duan, The heat kernel and Green function of the sub-Laplacian on the Heisenberg group, in Pseudo-Differential Operators, Generalized Functions and Asymptotics, 231 (2013), 55-75.

    Article  MathSciNet  MATH  Google Scholar 

  5. G.B. Folland, Spherical harmonic expansion of the Poisson-Szeg\(\ddot{o}\) kernel for the ball, Proc. Am. Math. Soc. (1975), 47(2), 401-407.

    MATH  Google Scholar 

  6. A. Nikiforov and V. Ouvarov, Fonction speciales de la Physique mathematique, Edition Mir (1983).

  7. H. Koch, and F. Ricci, Spectral projections for the twisted Laplacian, Studia Mathematica, 2007, 180(2), 103-110.

    Article  MathSciNet  MATH  Google Scholar 

  8. W. Rudin, Function theory in the unit ball of \({\mathbb{C}}n\), Springer-Verlag, New York, 1980.

    Book  MATH  Google Scholar 

  9. R.S. Strichartz, Harmonic analysis as spectral theory of Laplacians, J. Funct. Anal. 87 (1989), 51-148.

    Article  MathSciNet  MATH  Google Scholar 

  10. S. Thangavelu, Poisson transform for the Heisenberg group and eigenfunctions of sublaplacian, Math Ann, (2006), 335, 879-899.

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Thangavelu, Harmonic analysis on the Heisenberg group, Prog. Math. 159, Birkhauser, Boston (1998).

  12. F. G. Tricomi, Fonctions hypergéométriques confluentes, Mém. Sci. Math, 140 (2009).

  13. M.W. Wong, Weyl transforms, the heat kernel and Green function of a degenerate elliptic operator, Ann. Global Anal. Geom. 28 (2005), 271-283.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Laboratory of Partial Differential Equations Algebra and Spectral Geometry, Ibn Tofail University, Kenitra, Morocco

    Adil Bouhrara & Samir Kabbaj

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  1. Adil Bouhrara
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  2. Samir Kabbaj
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Correspondence to Adil Bouhrara.

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Communicated by Rahul Roy.

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Bouhrara, A., Kabbaj, S. On the complex twisted Laplacian on \( \mathbb {C}^n\) and Poisson transform for the Heisenberg group. Indian J Pure Appl Math 54, 966–979 (2023). https://doi.org/10.1007/s13226-022-00316-8

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  • DOI: https://doi.org/10.1007/s13226-022-00316-8

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