Mathematical Sciences: Complex Analysis and Harmonic        Analysis
{'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 will be directed at problems arising in the theories of            several complex variables and harmonic analysis.  The research                  represents a continuation of earlier investigations following                   three themes: convolution equations, interpolation problems and                 ideals generated by exponential polynomials.                                            The background for problems of convolution and interpolation            can be traced to fundamental questions of convolutions of a                     single function by a collection of measures vanishing                           simultaneously, and whether the system can be analyzed through                  the joint spectrum of the measures' Fourier transforms.  Work on                such questions led to conditions which, while correct, are not                  easily verified.  The principal investigator will pursue several                concrete-type criteria on which there has already been partial                  success.  One particular impediment leads to a number-theoretic                 question which estimates the distance between roots of                          exponential polynomials.  Some progress has been made here which                may lead to applications to delay-type partial differential                     equations.                                                                              A different type of convolution problem which appears in                other contexts is that of the Pompeiu problem.  In its                          rudimentary form, the problem concerns integrals of an unknown                  function taken over some geometric shape as the shape (or shapes)               are moved by rigid motions.  Whether or not one can recover the                 function from these calculations is a deep question whose                       resolution is known only in cases involving considerable                        symmetry.  The principal investigator has expanded his work to                  the setting of manifolds (symmetric spaces).  He has shown that                 the question of failure of the Pompeiu problem is directly                      related to a Neumann boundary value problem for an elliptic                     partial differential equation.  While there are many applications               of the result, a condition is imposed on the manifolds - they                   must be of rank 1.  Work will be done in easing this requirement.               This research has close connections to tomographic                              investigations.
{'FirstName': 'Carlos', 'LastName': 'Berenstein', 'PI_MID_INIT': 'A', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Carlos A Berenstein', 'EmailAddress': 'carlos@isr.umd.edu', 'NSF_ID': '000120572', 'StartDate': '06/15/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'University of Maryland, College Park', 'CityName': 'COLLEGE PARK', 'ZipCode': '207425100', 'PhoneNumber': '3014056269', 'StreetAddress': '3112 LEE BUILDING', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Maryland', 'StateCode': 'MD', 'CONGRESSDISTRICT': '04', 'CONGRESS_DISTRICT_ORG': 'MD04', 'ORG_UEI_NUM': 'NPU8ULVAAS23', 'ORG_LGL_BUS_NAME': 'UNIVERSITY OF MARYLAND, COLLEGE PARK', 'ORG_PRNT_UEI_NUM': 'NPU8ULVAAS23'}
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{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}
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