Mathematical Sciences: Harmonic Analysis, Special Functions and Separation of Variables
{'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}
Separation of variables is the best known method of reducing               partial differential equations to simpler form.  It is taught in                undergraduate mathematics courses and is often viewed as nothing                more than a serendipitous accident.  There are, in fact, deep                   mathematical and physical reasons why separation of variables                   works and why it actually applies across a large class of                       equations.  The purpose of this work is to continue a long-term                 investigation into the circumstances and applicable methods for                 treating equations which can be decomposed.                                          The work divides into several parts.  First is the problem                 of determining a general definition of variable separation that                 applies to all (systems of) partial differential equations and                  working out the structure theory of possible separation types.                  Second is the problem of intrinsic characterization of separable                coordinates.  For Hamilton-Jacobi and Schrodinger equations this                problem is essentially solved.  For systems of equations such as                the Dirac and linear elasticity equations, it remains open.  Work               will continue in this area.  Finally, there is the problem of                   determining the special functions that arise when variables are                 separated in a particular equation and establishing properties of               these functions.  Particular emphasis is placed on those                        properties which are a consequence of the symmetry of the                       associated equation.
{'FirstName': 'Willard', 'LastName': 'Miller', 'PI_MID_INIT': None, 'PI_SUFX_NAME': 'Jr.', 'PI_FULL_NAME': 'Willard Miller', 'EmailAddress': 'miller@math.umn.edu', 'NSF_ID': '000312316', 'StartDate': '06/15/1989', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Minnesota-Twin Cities', 'CityName': 'MINNEAPOLIS', 'ZipCode': '554552009', 'PhoneNumber': '6126245599', 'StreetAddress': '200 OAK ST SE', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Minnesota', 'StateCode': 'MN', 'CONGRESSDISTRICT': '05', 'CONGRESS_DISTRICT_ORG': 'MN05', 'ORG_UEI_NUM': 'KABJZBBJ4B54', 'ORG_LGL_BUS_NAME': 'REGENTS OF THE UNIVERSITY OF MINNESOTA', 'ORG_PRNT_UEI_NUM': None}
{'Name': None, 'CityName': None, 'StateCode': None, 'ZipCode': None, 'StreetAddress': None, 'CountryCode': None, 'CountryName': None, 'StateName': None, 'CountryFlag': None, 'CONGRESSDISTRICT': None, 'CONGRESS_DISTRICT_PERF': '""'}
{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8823054.xml'}