Mathematical Sciences: Orthogonal Polynomials and Their     Applications
{'Code': '03040102', 'Directorate': {'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'John V. Ryff'}
Work will concentrate primarily on problems arising in real,               complex and matrix valued orthogonal polynomials.  This includes                an analysis of polynomials and associated quantities such as                    higher order derivatives, Christoffel functions, Cotes numbers                  and roots of orthogonal polynomials at singular points of the                   support of the measure (which determines the orthogonality).                    Related work will also look at points where the absolutely                      continuous component of the measure vanishes and the nature of                  these quantities near the endpoints of support.  Applications of                this work will be made to tail estimates of statistical                         distributions.  When orthogonal polynomials are given as                        eigenfunctions of Jacobi matrices, the corresponding measure is                 the spectral measure of the matrix.  The logarithmic                            integrability of the absolutely continuous component of the                     measure (Szego's condition) is not controllable.  A major goal of               this project is to find necessary and sufficient conditions on                  the matrix so that the integrability condition will be satisfied.               Examples of compact perturbations of constant Jacobi matrices                   having purely singular spectral measures have been discovered.                  Work is progressing on the relevant inverse question: to find                   conditions on any spectral measure to see if it arises from a                   compact perturbation of a constant Jacobi matrix.  Efforts will                 also be made in extending the classical Szego theory to take in                 the case of measures supported on curves in the complex plane, to               study the behavior of orthogonal polynomials in classical                       Lebesgue spaces (rather than pointwise) and to continue research                on relating coefficients in three-term recursive definitions of                 polynomials with the corresponding spectral measures.                                Applications to least square prediction theory of discrete-                time theory stationary stochastic processes and signal processing               are planned.
[{'FirstName': 'William', 'LastName': 'Bauldry', 'EmailAddress': 'bauldrywc@appstate.edu', 'StartDate': '07/15/1988', 'EndDate': None, 'RoleCode': 'Co-Principal Investigator'}, {'FirstName': 'Paul', 'LastName': 'Nevai', 'EmailAddress': 'pali+@osu.edu', 'StartDate': '07/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}]
{'Name': 'Ohio State University Research Foundation -DO NOT USE', 'CityName': 'Columbus', 'ZipCode': '432101016', 'PhoneNumber': '6146888734', 'StreetAddress': '1960 KENNY RD', 'CountryName': 'United States', 'StateName': 'Ohio', 'StateCode': 'OH'}
[{'Code': '1261', 'Text': 'CLASSICAL ANALYSIS'}, {'Code': '1271', 'Text': 'COMPUTATIONAL MATHEMATICS'}]
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8814488.xml'}