Bi-orthogonal Polynomials on the Unit Circle, Regular Semi-Classical Weights and Integrable Systems
نویسندگان
چکیده
منابع مشابه
Bi-orthogonal Polynomials on the Unit Circle, Regular Semi-classical Weights and Integrable Systems
Abstract. The theory of bi-orthogonal polynomials on the unit circle is developed for a general class of weights leading to systems of recurrence relations and derivatives of the polynomials and their associated functions, and to functional-difference equations of certain coefficient functions appearing in the theory. A natural formulation of the Riemann-Hilbert problem is presented which has a...
متن کاملBi-orthogonal systems on the unit circle, regular semi-classical weights and integrable systems - II
We 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 ,. .. ...
متن کاملBi-orthogonal systems on the unit circle, regular semi-classical weights and the discrete Garnier equations
We demonstrate that a system of bi-orthogonal polynomials and their associated functions corresponding to a regular semi-classical weight on the unit circle constitute a class of general classical solutions to the Garnier systems by explicitly constructing its Hamiltonian formulation and showing that it coincides with that of a Garnier system. Such systems can also be characterised by recurrenc...
متن کاملSchur Functions and Orthogonal Polynomials on the Unit Circle
We apply a theorem of Geronimus to derive some new formulas connecting Schur functions with orthogonal polynomials on the unit circle. The applications include the description of the associated measures and a short proof of Boyd’s result about Schur functions. We also give a simple proof for the above mentioned theorem of Geronimus. 1. Schur functions In what follows we adopt the following nota...
متن کاملSchur Flows and Orthogonal Polynomials on the Unit Circle
Abstract. The relation between the Toda lattices and similar nonlinear chains and orthogonal polynomials on the real line has been elaborated immensely for the last decades. We examine another system of differential-difference equations known as the Schur flow, within the framework of the theory of orthogonal polynomials on the unit circle. This system can be displayed in equivalent form as the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Constructive Approximation
سال: 2006
ISSN: 0176-4276,1432-0940
DOI: 10.1007/s00365-005-0616-7