M.Sc Thesis

M.Sc StudentLavner Hagai
SubjectProblems in Multiple Pointwise Convergence
DepartmentDepartment of Mathematics
Supervisor PROF. Tamar Ziegler


In this work we the study almost everywhere convergence of certain multiple ergodic averages.

Convergence in norm is known, and implies in particular the multiple recurrence theorem of Furstenberg.

However, almost sure convergence is known only for the double ergodic averages. Here we obtain an improved convergence result for the double ergodic averages, analogous to the Wiener-Wintner theorem. As an application we prove the asymptotic orthogonality of the Mobius function to sequences arising from dynamical systems.