کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4638502 1632007 2015 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Multiple orthogonal polynomials on the unit circle. Normality and recurrence relations
ترجمه فارسی عنوان
چندجملهای چندگانه در دایره واحد. روابط عادی و عادی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
چکیده انگلیسی
This paper is a second contribution to this field. We first obtain a determinantal formula for MOPUC (multiple Heine's formula) and we analyze the concept of normality, from a dynamical point of view and by presenting a first example: the combination of the Lebesgue and Rogers-Szegő measures. Secondly, we deduce recurrence relations for MOPUC without using Riemann-Hilbert analysis, only by considering orthogonality conditions. This new approach allows us to complete the recurrence relations in the situation when the origin is a zero of MOPUC, a case that was not considered before. As a consequence, we give an appropriate definition of multiple Verblunsky coefficients. A multiple version of the well known Szegő recurrence relation is also obtained. Here, the coefficients that appear in the recurrence satisfy certain partial difference equations that are used to present a recursive algorithm for the computation of MOPUC. A discussion on the Riemann-Hilbert approach that also includes the case when the origin is a zero of MOPUC is presented. Some conclusions and open questions are finally mentioned.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 284, 15 August 2015, Pages 115-132
نویسندگان
, , ,