The Euclidean Case

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 2 in Offbeat Integral Geometry on Symmetric Spaces, 2013, pp 43-83 from Springer

Abstract: 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.

Keywords: Entire Function; Inversion Formula; Algebraic Polynomial; Integral Geometry; Nonzero Function (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_2

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DOI: 10.1007/978-3-0348-0572-8_2

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