On functions with zero spherical means of complex hyperbolic spaces

DOI10.1007/BF02676722zbMath1008.43008OpenAlexW1970654292MaRDI QIDQ5942009

Vitalii Vladimirovich Volchkov

Publication date: 26 March 2003

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02676722

zbMATH Keywords

spherical harmonicsLaplace-Beltrami operatorhypergeometric functionspherical meanscomplex hyperbolic spaceBergman metricsbiholomorphic mappingPoisson kernel in a ballPompeiu setProizvolov problemtwo-radii theorem

Mathematics Subject Classification ID

Harmonic analysis on homogeneous spaces (43A85)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Uniqueness theorems for some classes of functions with zero spherical means
• Morera type theorems on the unit disc
• On a problem of Zalcman and its generalizations
• The final version of the mean value theorem for harmonic functions
• Extremal cases of the Pompeiu problem.
• Two radii theorems on constant curvature spaces
• Inversion of the local Pompeiu transform in real and complex hyperbolic spaces: Case of two balls
• Mean-value theorems for a class of polynomials
• NEW THEOREMS ON THE MEAN FOR SOLUTIONS OF THE HELMHOLTZ EQUATION
• The finiteness of compact varieties in $C^n$
• Solution of the support problem for several function classes
• Injectivity sets for the Radon transform over a sphere
• ON THE NUMBER OF TRIANGULATION SIMPLEXES
• A definitive version of the local two-radii theorem

This page was built for publication: On functions with zero spherical means of complex hyperbolic spaces