The Pompeiu Transform on Symmetric Spaces and Groups

Valery V. Volchkov and Vitaly V. Volchkov
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Valery V. Volchkov: Donetsk National University, Department of Mathematics
Vitaly V. Volchkov: Donetsk National University, Department of Mathematics

Chapter Chapter 8 in Offbeat Integral Geometry on Symmetric Spaces, 2013, pp 497-526 from Springer

Abstract: 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.

Keywords: Symmetric Space; Heisenberg Group; Principal Series; Geodesic Ball; Plancherel Measure (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-0572-8_13

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DOI: 10.1007/978-3-0348-0572-8_13

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