Document Type
Article
Publication Date
1-1-2014
Abstract
We review some basic facts about the λ-cosine transforms with odd kernel on the unit sphere S n-1 in ℝ n . These transforms are represented by the spherical fractional integrals arising as a result of evaluation of the Fourier transform of homogeneous functions. The related topic is the hemispherical transform which assigns to every finite Borel measure on S n-1 its values for all hemispheres. We revisit the known facts about this transform and obtain new results. In particular, we show that the classical Funk- Radon-Helgason inversion method of spherical means is applicable to the hemispherical transform of L p -functions. © 2014 Versita Warsaw and Springer-Verlag Wien.
Publication Source (Journal or Book title)
Fractional Calculus and Applied Analysis
First Page
765
Last Page
806
Recommended Citation
Rubin, B. (2014). The λ-cosine transforms with odd kernel and the hemispherical transform. Fractional Calculus and Applied Analysis, 17 (3), 765-806. https://doi.org/10.2478/s13540-014-0198-9