6 papers
Operator ergodic theorems with Möbius "weights"
El Houcein El Abdalaoui, Michael Lin
Motivated by Sarnak's conjecture in topological dynamics for the Möbius function , we study, for a power-bounded on a Banach space , the weak convergence $$ (*) \qquad \q…
Spectra of averages of unitary representations of LCA groups
Guy Cohen, Michael Lin
Let be a locally compact Abelian (LCA) group with dual group , and let be a probability measure on (the Borel sets of) . Given a unitary representation $\{U(t): t \in…
Doeblin's condition, -mixing and spectra of convolution operators on the circle
Guy Cohen, Michael Lin
We study the asymptotic behavior of Markov operators defined by convolution with a probability measure on the unit circle . We prove that when is adapted,…
The Positive Mass Theorem for Creased Initial Data
Demetre Kazaras, Marcus Khuri, Michael Lin
We establish a spacetime positive mass theorem and rigidity statement for asymptotically flat spin initial data sets with a codimension one singularity controlled by a matching Bar…
Mean ergodic theorems in and ,
el Houcein el Abdalaoui, Michael Lin
Let be the Koopman operator of a measure preserving transformation of a probability space . We study the convergence properties of the averages $M_nf:=\frac1n\sum_…
Uniform ergodicity and the one-sided ergodic Hilbert transform
Guy Cohen, Michael Lin
Let be a bounded linear operator on a Banach space satisfying . We prove that is uniformly ergodic if and only if the one-sided ergodic Hilbert transfo…