Mathematical Sciences: Lifting Properties of Invariant      Kernels and Applications
{'Code': '03040102', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff', 'PO_EMAI': None, 'PO_PHON': None}
This research will focus on applications of the theory of               generalized Toeplitz kernels to problems in analysis and                        probability theory, especially to weighted norm inequalities and                moment problems.                                                                        One direction this work takes concerns stationarity of                  stochastic processes.  A generalized notion of stationarity for                 such processes arises from the theory of singular integrals                     through the consideration of generalized Toeplitz kernels.  The                 characterization of the processes having covariance kernels that                are such was given using lifting properties of the kernels.  The                classical stationary processes being those that have covariance                 kernels that are Toeplitz or invariant occur as special cases.                  Present work is planned in dealing with kernels that are                        invariant under one-parameter groups of transformations and the                 treatment of bidimensional interpolation problems with a goal of                providing a bidimensional version of the classical Helson-Szego                 theorem of prediction theory.                                                           A second application of this work will be sought in the                 study of lacunary coefficients of classes of analytic functions.                The prototype of the theory is in the work of Paley which asserts               that functions in Hardy space with lacunary coefficients are                    square integrable                                                               .  A dual result derives from Hankel forms which are effectively                the mirror images of Toeplitz forms.  New results are expected                  which can be translated into weighted norm inequalities for                     Fourier transforms.                                                                     In addition to prediction theory this work relates to ideas             in quantum theory, scattering structures and systems theory, as                 well as moment problems in engineering.
{'FirstName': 'Cora', 'LastName': 'Sadosky', 'PI_MID_INIT': None, 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Cora Sadosky', 'EmailAddress': 'cs@scs.howard.edu', 'NSF_ID': '000233488', 'StartDate': '09/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Mathematical Sciences Research Institute', 'CityName': 'BERKELEY', 'ZipCode': '947205070', 'PhoneNumber': '5106420143', 'StreetAddress': '17 GAUSS WAY', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'California', 'StateCode': 'CA', 'CONGRESSDISTRICT': '12', 'CONGRESS_DISTRICT_ORG': 'CA12', 'ORG_UEI_NUM': 'LWLJAPATKEL8', 'ORG_LGL_BUS_NAME': 'MATHEMATICAL SCIENCES RESEARCH INSTITUTE', 'ORG_PRNT_UEI_NUM': 'LWLJAPATKEL8'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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