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
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کلمات کلیدی
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-SzegÅ 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 SzegÅ 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
Journal: Journal of Computational and Applied Mathematics - Volume 284, 15 August 2015, Pages 115-132
نویسندگان
Ruymán Cruz-Barroso, Carlos DÃaz Mendoza, Ramón Orive,