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Poisson formulas for circular functions on some groups of type H

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Abstract

Explicit Poisson kernels are found for the subelliptic Dirichlet problem with boundary data satisfying certain symmetry conditions on balls and halfspaces in some Heisenberg type groups.

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References

  1. Gaveau B, Greiner P, Vauthier J. Polynômes harmoniques et problème de Dirichlet de la boule du groupe de Heisenberg en présence de symétrie radiale. Bull Sc Math, 1984, 108: 337–354

    MathSciNet  Google Scholar 

  2. Korányi A, Reimann H M. Horizontal normal vectors and conformal capacity of spherical rings in the Heisenberg group. Bull Sc Math, 1987, 111: 3–21

    Google Scholar 

  3. Kaplan A. Fundamental solutions for a class of hypoelliptic PDE generated by composition of quadratic forms. Trans AMS, 1980, 258: 147–153

    Article  Google Scholar 

  4. Garofalo N, Vassilev D. Symmetry properties of positive solutions of Yamabe-type equations on groups of Heisenberg type. Duke Math J, 2001, 106: 411–448

    Article  MathSciNet  Google Scholar 

  5. Gaveau B. Principe de moindre action, propagation da la chaleur et estimées sous-elliptiques sur certains groupes nilpotents. Acta Math, 1977, 139: 95–153

    Article  MathSciNet  Google Scholar 

  6. Cowling M, Dooley A H, Korányi A, et al. H-type groups and Iwasawa decompositions. Adv Math, 1991, 87: 1–41

    Article  MathSciNet  Google Scholar 

  7. Erdélyi A, et al. Higher transcendental functions. New York: McGraw-Hill, 1953

    Google Scholar 

  8. Korányi A. Kelvin transforms and harmonic polynomials on the Heisenberg group. J Funct Analysis, 1982, 49: 177–185

    Article  Google Scholar 

  9. Garofalo N, Vassilev D. Regularity near the characteristic set in the non-linear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups. Math Ann, 2000, 318: 453–516

    Article  MathSciNet  Google Scholar 

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Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

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Korányi, A. Poisson formulas for circular functions on some groups of type H . SCI CHINA SER A 49, 1683–1695 (2006). https://doi.org/10.1007/s11425-006-2065-6

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  • DOI: https://doi.org/10.1007/s11425-006-2065-6

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