On the spherical slice transform

We study the spherical slice transform [Formula: see text] which assigns to a function f on unit sphere S n in integrals of over cross-sections by k-dimensional affine planes passing through north pole (0,…, 0, 1). These transforms are known when k = n. consider all 2 ≤ and obtain an explicit formula connecting with classical (k − 1)-plane Radon–John text]. Using this connection, facts for R k−1 , like inversion formulas, support theorems, representation zonal functions, some others, reformulated