Unit:
Κατεύθυνση Θεωρητικά ΜαθηματικάLibrary of the School of Science
Author:
Lamprinakis Georgios
Supervisors info:
Γατζούρας Δημήτριος, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Γιαννόπουλος Απόστολος, Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Δοδός Παντελής, Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών, Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών
Original Title:
Ergodic averages along cubes
Translated title:
Ergodic averages along cubes
Summary:
We study the convergence of the ergodic averages of the integral of the product of 2^k functions and the L^2-convergence of the ergodic averages of the product of 2^k -1 functions, for k = 2, 3. These averages are taken along cubes whose sizes tend to infinity. For each average we show that it is sufficient to prove the convergence for special systems, the characteristic factors. We build these factors in a general way, independent of the type of the average. From the first convergence result a combinatorial interpretation can be derived for the arithmetic structure inside a set of integers of positive upper density. For the case k=3, further reduction is needed, associating each of the factors to some special systems, known as nilsystems and it suffices to prove the convergence for these systems.
Main subject category:
Science
Keywords:
nonconventional ergodic averages, 'cubes', characteristic factors, nilsystems
