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Information × Registration Number 0201U001352, 0197U016647 , R & D reports Title Integrable systems, spectral transformations, nonlinear algebras and special functions popup.stage_title Head Zhedanov O.S., Registration Date 31-01-2001 Organization A.A. Galkin Physics and Engineering Institute of National Academy of Science of the Ukraine popup.description2 The main result of the project is establishing of unified approach of spectral (Darboux) transformartions to three wide classes of functions: orthogonal polynomials, biorthogonal Laurent polynomials and biorthogonal rational functions. 1. In theory of orthogonal polynomials it was shown that the so-called semi-classical and Laguerre-Hahn classes of these polynomials arise as self-similar closure conditions of the chain of spectral transformations. 2. In theory of Laurent biorthogonal polynomials a criterion for classical polynomials was found. The theory of spectral transformations of such objects was developed. 3. New class of rational functions which are biorthogonal on elliptic grids was explicitly constructed. Product Description popup.authors popup.nrat_date 2020-04-02 Close