Abstract
In many questions of integral geometry there arise operators of the following type: \( Af(x)\,=\, \frac{1}{{\sqrt \pi }}\,\int\nolimits_0^x {}\, \frac{{tf(t)}} {{\sqrt {x^2 - t^2 } }}dt,\,x \,> \,0.\) This is the classical Abel transform, which can be explicitly inverted.
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© 2013 Springer Basel
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Volchkov, V.V., Volchkov, V.V. (2013). The Euclidean Case. In: Offbeat Integral Geometry on Symmetric Spaces. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0572-8_2
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DOI: https://doi.org/10.1007/978-3-0348-0572-8_2
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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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