Abstract
We construct an analog of the Poincaré model for a quaternion hyperbolic space.
Similar content being viewed by others
REFERENCES
S. Helgason, Groups and Geometric Analysis [Russian translation], Mir, Moscow (1987).
H. C. Wang, “Two point homogeneous spaces,” Ann. Math., 55, 177–191 (1952).
J. Tits, “Sur certains classes d'espaces homogenes de groupes de Lie,” Acad. Roy. Belg. Cl. Sci. Mem. Coll., 29, No. 3, 157–183 (1955).
J. A. Wolf, Spaces of Constant Curvature [Russian translation], Nauka, Moscow (1982).
S. G. Krantz, Function Theory of Several Complex Variables, Wiley, New York (1982).
B. V. Shabat, Introduction to Complex Analysis [in Russian], Nauka, Moscow (1985).
V. V. Volchkov, “A final version of a local theorem on two radii,” Mat. Sb., 186, No. 6, 15–34 (1995).
V. V. Volchkov, “New theorems on two radii in the theory of harmonic functions,” Izv. Ros. Akad. Nauk, Ser. Mat., 58, No. 1, 182–194 (1994).
V. V. Volchkov, “On one Zalcman problem and its generalizations,” Mat. Zametki, 53, No 2, 30–36 (1993).
Vit. V. Volchkov, “Theorems on solid spherical means on complex hyperbolic spaces,” Dop. Nats. Akad. Ukr., No. 4, 7–10 (2000).
M. Harchaoui, “Inversion de la transformation de Pompeiu locale dans les espaces hyperboliques reel et complete (Cas de deux boules),” J. Anal. Math., 67, 1–37 (1995).
C. A. Berenstein and D. Struppa, Complex analysis and equations in convolutions,” in: VINITI Series in Contemporary Problems in Mathematics. Fundamental Trends, Vol. 54, VINITI, Moscow (1989), pp. 5–111.
L. Zalcman, “A bibliographic survey of the Pompeiu problem,” in: B. Fuglede et. al. (editors), Approximate Solutions of Partial Differential Equations (1992), pp. 185–194.
I. Netuka and J. Vesely, “Mean value property and harmonic functions,” in: Classical and Modern Potential Theory and Applications, Kluwer, Dordrecht (1994), pp. 359–398.
A. T. Fomenko, Symplectic Geometry. Methods and Applications [in Russian], Moscow University, Moscow (1988).
B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry [in Russian], Nauka, Moscow (1979).
D. P. Zhelobenko and A. I. Shtern, Representations of Lie Groups [in Russian], Nauka, Moscow (1983).
W. Rudin, Function Theory in the Unit Ball in ℂn [Russian translation], Mir, Moscow (1984).
C. A. Berenstein and L. Zalcman, “Pompeiu's problem on symmetric spaces,” Comment. Math. Helv., 55, 593–621 (1980).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Volchkov, V.V. An Analog of the Poincaré Model for a Quaternion Hyperbolic Space. Ukrainian Mathematical Journal 53, 1618–1625 (2001). https://doi.org/10.1023/A:1015287725623
Issue Date:
DOI: https://doi.org/10.1023/A:1015287725623