The theory of orthogonal polynomials on the unit circle (OPUC) dates back to Szegö's work of 1915-21, and has been given a great impetus by the recent work of Simon, in particular his two-volume book [Si4], [Si5], the survey paper (or summary of the book) [Si3], and the book [Si9], whose title we allude to in ours. Simon's motivation comes from spectral theory and analysis. Another major area of application of OPUC comes from probability, statistics, time series and prediction theory; see for instance the book by Grenander and Szegö [GrSz]. Coming to the subject from this background, our aim here is to complement [Si3] by giving some probabilistically motivated results. We also advocate a new definition of long-range dependence.AMS 2000 subject classifications. Primary 60G10, secondary 60G25.
The pressure and temperature history of the Tertiary Shimanto belt of south‐west Japan has been elucidated by analysing fluids trapped in quartz crystals which grew syn‐kinematically along late‐stage brittle faults. The samples come from three areas that span the Paleogene exposures on the Muroto Peninsula of Shikoku Island. Applying microthermometric and laser Raman microsampling techniques to coeval water‐rich and carbonic fluid inclusions, we have constrained the pressure and temperature conditions that accompanied a widespread and kinematically distinct phase of deformation. The results suggest elevated geothermal gradients during late‐stage deformation, conditions that are in disaccord with previous plate reconstructions that have depicted old, thermally mature Pacific crust subducting beneath Eurasia during the early to middle Tertiary. These conditions can most easily be accounted for by including an additional plate boundary in the western Pacific during Paleogene time. Plate reconstructions that include the Kula plate in this region are therefore consistent with our findings. In addition, our results provide clues to the conditions that likely accompany seismogenic deformation at active convergent plate boundaries.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.