Behavior of renormalized Feynman amplitudes under scale transformations $\lambda\varphi^4(x)$

A study is made of the behavior of the Feynman amplitudes renormalized by Speer's analytic regularization method under scale transformations in the $\lambda\varphi^4(x)$ theory with $m^2\ne0$. It is shown that logarithmic terms arise as a result of regularization under scale transformations of the renormalized Feynman amplitudes.