The circle transform on trees
Enrico Casadio Tarabusi, Simon G. Gindikin, and Massimo A. Picardello
We consider the overdetermined problem of integral geometry on trees given by the transform that integrates functions on a tree over circles, and exhibit difference equations that describe the range. We then show how this problem modifies if we restrict the transform to some natural subcomplex of the complex of circles, proving inversion formulas and characterizing ranges.