کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4582319 1413318 2016 40 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Orthogonal polynomials and perturbations on measures supported on the real line and on the unit circle. A matrix perspective
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Orthogonal polynomials and perturbations on measures supported on the real line and on the unit circle. A matrix perspective
چکیده انگلیسی

The connection between measures supported on the real line (resp. on the unit circle), Hankel (resp. Toeplitz) matrices, Jacobi (resp. Hessenberg and CMV) matrices, Stieltjes (resp. Carathéodory) functions constitutes a key element in the analysis of orthogonal polynomials on the real line (resp. on the unit circle). In the present contribution, we focus our attention on perturbations of the measures supported either on the real line or the unit circle and their consequences on the behavior of the corresponding sequences of orthogonal polynomials and the matrices associated with the multiplication operator in terms on those polynomial bases. The matrix perspective related to such perturbations from the point of view of factorizations (LULU and QRQR) is emphasized. Finally, we show the role of spectral transformations in the analysis of some integrable systems.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Expositiones Mathematicae - Volume 34, Issue 3, 2016, Pages 287–326
نویسندگان
, ,