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math.SP2022
On spectral measures and convergence rates in von Neumann's Ergodic Theorem
M. Aloisio, S. L. Carvalho, C. R. de Oliveira +1
We show that the power-law decay exponents in von Neumann's Ergodic Theorem (for discrete systems) are the pointwise scaling exponents of a spectral measure at the spectral value~$…
math.SP2022
On the Fourier asymptotics of absolutely continuous measures with power-law singularities
M. Aloisio, S. L. de Carvalho, C. R. de Oliveira +1
We prove sharp estimates on the time-average behavior of the squared absolute value of the Fourier transform of some absolutely continuous measures that may have power-law singular…