1 citations · 4 across the 7 of their papers we have counts for
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Pointwise Convergence of Sequences of Singular Measures
Andrew Parrish, Joseph Rosenblatt
We investigate the almost everywhere convergence of sequences of convolution operators given by probability measures on . If this sequence of operators constitutes…
Ergodic Theory and Diophantine approximation for translation surfaces and linear forms
Jayadev Athreya, Andrew Parrish, Jimmy Tseng
We derive results on the distribution of directions of saddle connections on translation surfaces using only the Birkhoff ergodic theorem applied to the geodesic flow on the moduli…
Perturbation of Sparse Ergodic Averages
Andrew Parrish
We provide examples of a nested sequences of sets {S_n}, suitably sparse, residing in a group G, for which multidimensional averages fail converge pointwise for f in certain L^p sp…
Multivariable averaging on sparse sets
Patrick LaVictoire, Andrew Parrish, Joseph Rosenblatt
Nonstandard ergodic averages can be defined for a measure-preserving action of a group on a probability space, as a natural extension of classical (nonstandard) ergodic averages. W…
Pointwise Convergence of Ergodic Averages in Orlicz Spaces
Andrew Parrish
We show that for each Orlicz space properly contained in L^1 there is a sequence along which the ergodic averages converge for functions in the Orlicz space, but diverge for all f…