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LINEAR INDEPENDENCE OF A FINITE SET OF DILATIONS BY A ONE-PARAMETER MATRIX LIE GROUP
2013
International Journal of Pure and Applied Mathematics
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Let G = {e tA : t ∈ R} be a closed one-parameter subgroup of the general linear group of matrices of order n acting on R n by matrix-vector multiplication. We assume that all eigenvalues of A are rationally related. We study conditions for which the set f e t 1 A · , · · · , f e tmA · is linearly dependent in L p (R n ) with 1 ≤ p < ∞.
doi:10.12732/ijpam.v84i2.4
fatcat:e4ijwv7bijbbtivbx7udimqdci