The baker transformation as a nonlinear combination of pointwise mean expected value operators and the pointwise convergence to equilibrium (Q1125168)

Let \(p>1\) be an integer, and consider the baker transformation \(T\) defined on \((0,1]^2\) by \[ T(x, y)= px- \Biggl(\lfloor px\rfloor, {\lfloor px\rfloor+ y\over p}\Biggr). \] The authors express \(T\) as a nonlinear combination of pointwise mean expected value operators on the space of polynomials. They use this representation of \(T\) to show that the intrinsic rates of convergence to equilibrium can be obtained from the study of pointwise convergence.