Mathematical Sciences: Coding and Convergence in Ergodic andTheory
{'Code': '03040103', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'William Y. Velez', 'PO_EMAI': None, 'PO_PHON': None}
Petersen will continue his investigation of unusual                        pointwise ergodic theorems, in which sampling is done along a                   sequence of possibly non-integral times, singular weights are                   applied as in Hilbert transforms, averages are formed along a                   subsequence, or complex multipliers are allowed, as in Wiener-                  Wintner theorems. The connections of these questions with                       spectral properties of unitary flows and harmonic analysis will                 be explored. A unifying strategy is proposed for obtaining many                 such theorems at once as a consequence of a still to be                         determined smoothness property of spectral measures of measure-                 preserving transformations. Petersen will also continue his work                on symbolic dynamics, especially for countable alphabets and for                systems that arise in magnetic recording.                                            This project is mathematical research in ergodic theory.                   This theory is concerned with what happens on average over the                  long run when a suitable transformation of a suitable underlying                space is iterated many times. (Typically, the underlying space                  might be just a line segment, and the transformation might cut                  the line segment up into pieces, then stretch or shrink and                     rearrange them.) One point of view is to study the behavior of                  functions on the space when their arguments are repeatedly                      subjected to the transformation. It frequently happens that the                 averages of the iterates of the functions converge in a                         meaningful fashion. When the succesive iterates can be gotten                   from a flow, with continuous instead of discrete time, the limit                of the averaged iterates is under certain circumstances the                     continuous average over the flow. Petersen is interested in what                happens when the flow is sampled at other times besides the                     integer times that give the original sequence of iterates.
{'FirstName': 'Karl', 'LastName': 'Petersen', 'PI_MID_INIT': 'E', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Karl E Petersen', 'EmailAddress': 'petersen@math.unc.edu', 'NSF_ID': '000201433', 'StartDate': '06/15/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of North Carolina at Chapel Hill', 'CityName': 'CHAPEL HILL', 'ZipCode': '275995023', 'PhoneNumber': '9199663411', 'StreetAddress': '104 AIRPORT DR STE 2200', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'North Carolina', 'StateCode': 'NC', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'NC04', 'ORG_UEI_NUM': 'D3LHU66KBLD5', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL', 'ORG_PRNT_UEI_NUM': 'N8DMK1K4C2K5'}
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{'Code': '1262', 'Text': 'MODERN ANALYSIS'}
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