Generalized Sobolev orthogonal polynomials, matrix moment problems and   integrable systems
  We introduce a large class of Sobolev bi-orthogonal polynomial sequences arising from a $LU$-factorizable moment matrix and associated with a suitable measure matrix that characterizes the Sobolev bilinear form. A theory of deformations of Sobolev bilinear forms is also proposed. We consider both polynomial deformations and a class of transformations related to the action of linear operators on the entries of a given bilinear form. Transformation formulae among new and old polynomial sequences are determined. Finally, integrable hierarchies of evolution equations arising from the factorization of a time deformation of the moment matrix are presented. 
Gerardo Ariznabarreta, Manuel Ma\~nas and Piergiulio Tempesta
math.CA math-ph math.MP nlin.SI