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Rosenblatt, Joseph Argiris, Georgios 2015-09-28T15:19:30Z 2015-09-28T15:19:30Z 10000-01-01 2001 2001 We investigate two problems involving convergence in ergodic theory. The first problem is the following: Given a measure preserving transformation T and a weight function w(alpha) → 0 as alpha → 0, is there a p > 0 such that the expression w(alpha)#{ n : 1n k=1nfT kx >a } have a limit, a.s. or in norm, as alpha → 0 for all functions f ∈ Lp0 [0,1]? No, we show. Here # denotes counting measure and f's are taken to be mean-zero functions. We also consider similar questions for the more general operator w(alpha)#{n : 1nq k=1n f(Tk(x)) > alpha}, q > 1. The second problem addressed is to give arithmetic and probabilistic characterizations on the integer sequence ( nk) such that the series of ergodic differences k=1infinity ( Ank+1f-Ankf ), where An denotes the usual ergodic averages, converges unconditionally for all functions f in some Lp space. Made available in DSpace on 2015-09-28T15:19:30Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3023009.pdf: 2049317 bytes, checksum: 01968016ed63aca4d8c1d7ce4c221aa3 (MD5) Previous issue date: 2001 Embargo set by: Seth Robbins for item 88062 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 51 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001. http://hdl.handle.net/2142/86781 (MiAaPQ)AAI3023009 eng Mathematics Convergence in Ergodic Theory text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.