Abstract
Let L be the sublaplacian on the quaternion Heisenberg group N and T the Dirac type operator with respect to central variables of N. In this article, we characterize the ℍc-valued joint eigenfunctions of L and T having eigenvalues from the quaternionic Heisenberg fan.
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References
Helgason S. Eigenspaces of the Laplacian, integral representations and irreducibility. J Funct Anal, 1974, 17: 328–353
Helgason S. Topics in Harmonic Analysis on Homogeneous Spaces. In: Prog Math 13. Boston: Birkhäuser, 1981
Kashiwara M, Kowata A, Minemura K, et al. Eigenfunctions of invariant differential operators on a symmetric space. Ann Math, 1978, 107: 1–39
Liu H P, Zhang G K. Generalized Cauchy-Szego projections and the Heisenberg fan on the quaternionic Heisenberg group. Preprint, 2008
Morimoto M. Analytic Functionals on the Sphere. In: Trans Math Monogr 178. Providence, RI: Amer Math Soc, 1998
Strichartz R S. Harmonic analysis as spectral theory of Laplacians. J Funct Anal, 1989, 87: 51–148
Thangvelu S. Poisson transform for the Heisenberg group and eigenfunctions of sublaplacian. Math Ann, 2006, 335: 879–899
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Liu, H., Zhu, X. Joint eigenfunctions of invariant differential operators on the quaternion Heisenberg group. Sci. China Math. 56, 435–441 (2013). https://doi.org/10.1007/s11425-012-4510-z
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DOI: https://doi.org/10.1007/s11425-012-4510-z