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.
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© 2013 Springer Basel
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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
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DOI: https://doi.org/10.1007/978-3-0348-0572-8_13
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Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0571-1
Online ISBN: 978-3-0348-0572-8
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