A note on the Blaschke-Petkantschin formula, Riesz distributions, and drury's identity
Document Type
Article
Publication Date
12-19-2018
Abstract
The Blaschke-Petkantschin formula is a variant of the polar decomposition of the k-fold Lebesgue measure on R n in terms of the corresponding measures on k-dimensional linear subspaces of R n . 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.
Publication Source (Journal or Book title)
Fractional Calculus and Applied Analysis
First Page
1641
Last Page
1650
Recommended Citation
Rubin, B. (2018). A note on the Blaschke-Petkantschin formula, Riesz distributions, and drury's identity. Fractional Calculus and Applied Analysis, 21 (6), 1641-1650. https://doi.org/10.1515/fca-2018-0086