Selected Topics in Integral Geometry

By I. Gel'fand, S. Gindikin, M. Graev. 2003

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Some constructions for the fractional Laplacian on noncompact manifolds (2012, background): “Fourier transform and the fractional Laplacian We start by reviewing some basic facts about Fourier transform on hyperbolic space, see [29], [44] and [64].”
Mathematics of thermoacoustic tomography (2007, background): “ect to x: P(x,t) → q(s,t,ω) = Z x·ω=s p(x,t)dA(x), 31 where dAis the surface measure and ωis a unit vector in R3, this is well known to reduce the 3DLaplace operator ∆xto the second derivative ∂2/∂s2 [30, 38, 39, 40, 53, 54], and thus the 3Dwave equation to the string vibration problem. The measured”
Paneitz operators on hyperbolic spaces and high order Hardy-Sobolev-Maz'ya inequalities on half spaces (2019, background): “We begin by quoting some preliminary facts which will be needed in the sequel and refer to [1, 22, 30, 31, 33, 40] for more information about this subject.”