The Radon transform represents a function on a manifold by its
integrals over certain submanifolds. Integral transformations of
this kind have a wide range of applications in modern analysis,
integral and convex geometry, medical imaging, and many other
areas. Reconstruction of functions from their Radon transforms
requires tools from harmonic analysis and fractional
differentiation. This comprehensive introduction contains a
thorough exploration of Radon transforms and related operators when
the basic manifolds are the real Euclidean space, the unit sphere,
and the real hyperbolic space. Radon-like transforms are discussed
not only on smooth functions but also in the general context of
Lebesgue spaces. Applications, open problems, and recent results
are also included. The book will be useful for researchers in
integral geometry, harmonic analysis, and related branches of
mathematics, including applications. The text contains many
examples and detailed proofs, making it accessible to graduate
students and advanced undergraduates.
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