Bi-orthogonal systems on the unit circle, Regular Semi-Classical Weights and Integrable Systems - II

Simple item page
dc.creatorWitte, N. S.
dc.date2008-11-25
dc.date.accessioned2026-07-07T10:36:30Z
dc.date.available2026-07-07T10:36:30Z
dc.descriptionWe derive the Christoffel-Geronimus-Uvarov transformations of a system of bi-orthogonal polynomials and associated functions on the unit circle, that is to say the modification of the system corresponding to a rational modification of the weight function. In the specialisation of the weight function to the regular semi-classical case with an arbitrary number of regular singularities $ \{z_1, ..., z_M \} $ the bi-orthogonal system is known to be isomonodromy preserving with respect to deformations of the singular points. If the zeros and poles of the Christoffel-Geronimus-Uvarov factors coincide with the singularities then we have the Schlesinger transformations of this isomonodromic system. Compatibility of the Schlesinger transformations with the other structures of the system - the recurrence relations, the spectral derivatives and deformation derivatives is explicitly deduced. Various forms of Hirota-Miwa equations are derived for the $ τ$-functions or equivalently Toeplitz determinants of the system.
dc.descriptionto appear J. Approx. Theory
dc.identifierhttps://arxiv.org/abs/0811.4027
dc.identifierhttp://arxiv.org/abs/0811.4027
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/180073
dc.subjectClassical Analysis and ODEs
dc.subjectMathematical Physics
dc.subject05E35; 33C45; 34M55; 37K35; 39A05; 42A52
dc.titleBi-orthogonal systems on the unit circle, Regular Semi-Classical Weights and Integrable Systems - II
dc.typetext

Files

Collections

arXiv