Mathematical Sciences: Differential Equations in the ComplexDomain and Nevanlinna Theory
{'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}
Work on this project will develop three lines of                           mathematical research.  They include investigations into                        growth, oscillation and other properties of solutions of                        differential equations in the complex plane.  Particular                        emphasis will be placed on the determination of zero                            frequency and value distribution for solutions of linear                        equations.  Information regarding such characteristics are to                   be read from the coefficients of the equation and their                         magnitude. In addition to linear theory, studies will be made                   in estimating the growth of meromorphic solutions of                            algebraic differential equations.  Partial results have been                    obtained for second-order equations but nothing to date has                     been tried in obtaining uniform growth estimates for                            equations of higher order.                                                           A second line of work will be concerned with problems in                   harmonic analysis, with particular emphasis paid to the fine                    structure of absolutely convergent Fourier series.  This                        includes studies on sets where these series are restricted                      and the classification of the resulting function spaces.                        Work will also be done on problems related to removable sets                    for analytic functions.  These are sets, which can be deleted                   from the domain of an analytic function without changing the                    uniqueness of the function nor its values, which can be                         recovered across the removable set.                                                  The third thrust maintains continuing work on areas of                     harmonic measure and parabolic potential theory.                                Applications of harmonic measure to growth rates of analytic                    functions have grown sizeably in recent years because of very                   sharp estimates developed from research of this type.  In                       addition, results on parabolic potential theory provide                         general information concerning solutions of the heat equation                   by measurements of parabolic capacity.
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{'Name': 'University of Illinois at Urbana-Champaign', 'CityName': 'URBANA', 'ZipCode': '618013620', 'PhoneNumber': '2173332187', 'StreetAddress': '506 S WRIGHT ST', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Illinois', 'StateCode': 'IL', 'CONGRESSDISTRICT': '13', 'CONGRESS_DISTRICT_ORG': 'IL13', 'ORG_UEI_NUM': 'Y8CWNJRCNN91', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF ILLINOIS', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1987&All=true', 'xml': '8721813.xml'}