Objective Two great developments took place in the field of Orthogonal Polynomials (OP) in the last years. The first one based on the Riemann-Hilbert approach developed by the Courant group Deift,... It is well established now in the EU community thanks to Kriecherb auer, Kuijlaars, Van Assche... However it is opposite what concerns the second development: the sum rule method presented in [Killip, Simon, Ann. of Math., 2003]. Our main objective is to develop a general theory for OP beyond the Szego-class based on the sum rule approach; to apply the results in Inverse Scattering, Integrable Systems, Numerical Analysis.The project should overcome the mentioned EU lag to a great extent and encourage young mathematicians to do research in this promising topic. Another objective deals with a longstanding problem on limit periodicity of Jacobi matrices associated with measures on Julia sets. Ruelle operators and related concepts in OP form a rather open field of investigation. New technical and structural ideas might lead to astonishing developments. The applicant has an experience of a very fruitful collaboration with Prof. Peherstorfer (scientist in charge); their joint results are among the best in the field. His joint work with Volberg (MSU) on inverse scattering, with Bellissard, Geronimo on OP associated with iterations form an essential background for a successful realization of the project.To this end the Linz University is most likely one of the best places: the project has several different components and at al l of them Peherstorfer is a highly recognized expert. This, as well as the presence of strong groups of Functional and Numerical Analysis at the University produces an extra ordinary opportunity for the further scientific grow of the applicant. Realization of the project will reinforce also the scientific excellence of the community via the knowledge transfer, e.g. the applicant will deliver the newest powerful methods of Harmonic Analysis elaborated at MSU. Fields of science natural sciencesmathematicsapplied mathematicsnumerical analysis Keywords Cantor sets Jacobi matrix Julia sets approximation asymptotics integrable systems inverse scattering nodes orthogonal polynomials several intervals sparse linear systems Programme(s) FP6-MOBILITY - Human resources and Mobility in the specific programme for research, technological development and demonstration "Structuring the European Research Area" under the Sixth Framework Programme 2002-2006 Topic(s) MOBILITY-2.3 - Marie Curie Incoming International Fellowships (IIF) Call for proposal FP6-2002-MOBILITY-7 See other projects for this call Funding Scheme IIF - Marie Curie actions-Incoming International Fellowships Coordinator UNIVERSITAET LINZ Address Altenberger strasse 69 Linz Austria See on map Links Website Opens in new window EU contribution € 0,00
