Mathematical Sciences: Complex Analysis:  Computation and   Control.
{'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 project will focus on four areas of mathematical                      analysis.  Work will be done on estimating two-dimensional                      harmonic measure which is used in potential theory and in                       measuring growth of analytic functions.  At the present time                    estimates are known for the harmonic measure of curves in a                     disc meeting all radii in some sector.  The width of the                        maximal sector remains to be determined.  Theoretical and                       numerical efforts will be combined in this process.                                  Work will continue on problems of optimization using                       bounded holomorphic functions.  These investigations have                       been underway for several years.  They arise from certain                       engineering problems in optimal control and involve finding                     best approximations to given functions by bounded or                            continuous functions defined on a circle which have analytic                    extensions to the interior.                                                          A third, and more recent, goal of this project will                        involve methods for the computation of conformal maps.  There                   are many techniques extant for such computations and mappings                   of domains with smooth boundaries that generally have                           numerical approximants which converge rapidly.  The present                     work is concerned with approximation involving maps of                          domains with corners.  Recent progress has been encouraging                     although repetitions of the approximation process shows                         degradation after several passes.  Efforts will be made to                      single out the best boundary curves for which current methods                   are practical.  It is likely that these curves will fall into                   the class known as chord-arc curves which have restricted                       bending.                                                                             Finally, in a more theoretical vein, studies will be                       made into the existence and nature of inner functions which                     are constant on Gleason parts of the maximal ideal space of a                   disc.  While general theory indicates existence of such inner                   functions there is little known as to whether there are                         Blaschke products in this class.  Related to this work is a                     characterization of the zero-distribution of such products.                          In addition to applications to potential theory, this                      work adds to fundamental knowledge regarding numerical                          approximation schemes for partial differential equations.
{'FirstName': 'Donald', 'LastName': 'Marshall', 'PI_MID_INIT': 'E', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Donald E Marshall', 'EmailAddress': 'marshall@math.washington.edu', 'NSF_ID': '000466108', 'StartDate': '06/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Washington', 'CityName': 'SEATTLE', 'ZipCode': '981951016', 'PhoneNumber': '2065434043', 'StreetAddress': '4333 BROOKLYN AVE NE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Washington', 'StateCode': 'WA', 'CONGRESSDISTRICT': '07', 'CONGRESS_DISTRICT_ORG': 'WA07', 'ORG_UEI_NUM': 'HD1WMN6945W6', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF WASHINGTON', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8801675.xml'}