Linear Independence of a Finite Set of Dilations by a One-parameter Matrix Lie Group
Let G = {etA : t ∈ R} be a closed one-parameter subgroup of the general linear group of matrices of order n acting on Rn by matrix-vector multiplication. We assume that all eigenvalues of A are rationally related. We study conditions for which the set { f ( et1A· ) , · · · , f ( etmA· )} is linearly dependent in Lp (Rn) with 1 ≤ p <∞. AMS Subject Classification: 39B52