Abstract
The Blaschke-Petkantschin formula is a variant of the polar decomposition of the k-fold Lebesgue measure on ℝn in terms of the corresponding measures on k-dimensional linear subspaces of ℝn. We suggest a new elementary proof of this famous formula and discuss its connection with Riesz distributions associated with fractional powers of the Cayley-Laplace operator on matrix spaces. Another application of our proof is the celebrated Drury identity that plays a key role in the study of mapping properties of the Radon-John k-plane transforms. Our proof gives precise meaning to the constants in Drury’s identity and to the class of admissible functions.
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Rubin, B. A note on the Blaschke-Petkantschin formula, Riesz distributions, and Drury’s identity. FCAA 21, 1641–1650 (2018). https://doi.org/10.1515/fca-2018-0086
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DOI: https://doi.org/10.1515/fca-2018-0086