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Inversion Theorems for the local Pompeiu transformation in the quaternion hyperbolic space


Authors: Vit. V. Volchkov and N. P. Volchkova
Translated by: N. Yu. Netsvetaev
Original publication: Algebra i Analiz, tom 15 (2003), nomer 5.
Journal: St. Petersburg Math. J. 15 (2004), 753-771
MSC (2000): Primary 44A15, 53C65
DOI: https://doi.org/10.1090/S1061-0022-04-00830-1
Published electronically: July 29, 2004
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Abstract: A construction for inversion of the local Pompeiu transformation is obtained for the family consisting of two geodesic balls on the quaternion hyperbolic space.


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Additional Information

Vit. V. Volchkov
Affiliation: Donetsk National University, Department of Mathematical Analysis and Function Theory, Ulitsa A. Malyshko 3, Donetsk, 83053, Ukraine
Email: volchkov@univ.donetsk.ua

N. P. Volchkova
Affiliation: Donetsk National University, Department of Mathematical Analysis and Function Theory, Ulitsa A. Malyshko 3, Donetsk, 83053, Ukraine
Email: volchkov@univ.donetsk.ua

DOI: https://doi.org/10.1090/S1061-0022-04-00830-1
Keywords: Quaternionic hyperbolic space, Pompeiu transformation, theorem on two radii
Received by editor(s): October 28, 2002
Published electronically: July 29, 2004
Additional Notes: Partly supported by grant no. 01.07/00241 from the Foundation for Basic Research of Ukraine.
Article copyright: © Copyright 2004 American Mathematical Society

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