Abstract
New uniqueness theorems for periodic (in mean) functions on quaternion hyperbolic space are obtained.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
F. John, “Abhängigkeiten zwischen den Flächenintegralen einer stetigen Funktion,” Math. Ann., 111 (1935), 541–559.
F. John, Plane Waves and Spherical Means Applied to Partial Differential Equations, New York, 1955.
V. V. Volchkov, “The definitive version of the local two-radii theorem,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 186 (1995), no. 6, 15–34.
V. V. Volchkov, “New two-radii theorems in the theory of harmonic functions,” Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.], 58 (1994), no. 1, 182–194.
V. V. Volchkov, “Uniqueness theorems for multiple lacunary trigonometric series,” Mat. Zametki [Math. Notes], 51 (1992), no. 6, 27–31.
V. V. Volchkov, “Uniqueness theorems for some classes of functions with zero spherical means,” Mat. Zametki [Math. Notes], 62 (1997), no. 1, 59–65.
V. V. Volchkov, “Extremum versions of the Pompeiu problem,” Mat. Zametki [Math. Notes], 59 (1996), no. 5, 671–680.
V. V. Volchkov, “Mean-value theorems for a class of polynomials,” Sibirsk. Mat. Zh. [Siberian Math. J.], 35 (1994), no. 4, 737–745.
V. V. Volchkov, “Problems of Pompeiu type on manifolds,” Dokl. Akad. Nauk Ukrainy, 11 (1993), 9–12.
Vit. V. Volchkov, “Convolution equations on complex hyperbolic spaces,” Dop. NAN Ukrainy (2001), no. 2, 11–14.
V. V. Volchkov, “Two-radii theorems on spaces of constant curvature,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 347 (1996), no. 3, 300–302.
V. V. Volchkov, “Solution of the support problem for some classes of functions,” Mat. Sb. [Russian Acad. Sci. Sb. Math.], 188 (1997), no. 9, 13–30.
V. V. Volchkov, “The definitive version of the local two-radii theorem on hyperbolic spaces,” Izv. Ross. Akad. Nauk Ser. Mat. [Russian Acad. Sci. Izv. Math.], 65 (2001), no. 2, 3–26.
K. A. Berenstein and D. Struppa, “Complex analysis and convolution equations,” in: Itogi Nauki i Tekhniki [Progress in Science and Technology]. Current Problems in Mathematics. Fundamental Directions [in Russian], vol. 54, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform. (VINITI), Moscow, 1989, pp. 5–111.
L. Zalcman, “A Bibliographic Survey of the Pompeiu Problem,” in: Approximation by Solutions of Partial Differential Equations (1992), 185–194.
S. Helgason, Groups in Geometric Analysis, Orlando, 1984.
A. T. Fomenko, Symplectic Geometry. Methods and Applications [in Russian], Moskov. Gos. Univ., Moscow, 1988.
Vit. V. Volchkov and N. P. Volchkova, “Inversion of the local Pompeiu transformation on quaternion hyperbolic space,” Dokl. Ross. Akad. Nauk [Russian Acad. Sci. Dokl. Math.], 379 (2001), no. 5, 587–590.
Vit. V. Volchkov, “A realization of representations of symplectic groups Sp(n) in the spaces of homogeneous harmonic polynomials on the unit sphere in ℂ2n,” International Conference Dedicated to M. A. Lavrentiev on the Occasion of the Centenary of his Bidthday, Kiev, 31 October–3 November, 2000, Abstracts, pp. 72–73.
H. Bateman and A. Erdélyi, Higher Transcendental Functions, vol. 1, McGraw–Hill, New York–Toronto–London, 1953.
W. Rudin, Function Theory in the Unit Ball of ℂ n Springer-Verlag, Heidelberg, 1981.
N. Ya. Vilenkin, Special Functions and Group Representation Theory [in Russian], Second ed., Nauka, Moscow, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Volchkov, V.V. Uniqueness Theorems for Periodic (in Mean) Functions on Quaternion Hyperbolic Space. Mathematical Notes 74, 30–37 (2003). https://doi.org/10.1023/A:1025058830820
Issue Date:
DOI: https://doi.org/10.1023/A:1025058830820