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In this note, we study the Cauchy problem of the linear spatially homogeneousLandau equation with soft potentials. We prove that the solution to the Cauchyproblem enjoys the analytic regularizing effect of the time variable with an L2initial datum for positive time. So that the smoothing effect of Cauchy problemfor the linear spatially homogeneous Landau equation with soft potentials issimilar to the heat equation.

A remark about time-analyticity of the linear Landau equation with soft potential