Abstract
In this chapter we give a general definition of the Pompeiu transform and study its injectivity sets. In Section 8.1, we present sufficient conditions for injectivity of the Pompeiu transform on symmetric spaces of the non-compact type. In Section 8.2, the problem of the description of the injectivity sets for a broad class of distributions with support on the unit sphere is solved.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Basel
About this chapter
Cite this chapter
Volchkov, V.V., Volchkov, V.V. (2013). The Pompeiu Transform on Symmetric Spaces and Groups. In: Offbeat Integral Geometry on Symmetric Spaces. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0572-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0572-8_13
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0571-1
Online ISBN: 978-3-0348-0572-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)