On the small denominator problem for generalized Minkowski--Funk transforms

Rui Han, Yaghoub Rahimi

Rubin's generalized Minkowski--Funk transforms $M_t^{\alpha }$ on the sphere ${\mathbb{S}}^n$ give rise, for irrational radii $t=\cos (\beta \pi )$, to a small denominator problem governed by the asy…