THE CIRCLE TRANSFORM ON TREES

ENRICO CASADIO TARABUSI SIMON G. GINDIKIN MASSIMO A. PICARDELLO

Abstract. 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.