کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4607217 | 1631440 | 2013 | 26 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Asymptotic properties of extremal polynomials corresponding to measures supported on analytic regions
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let G be a bounded region with simply connected closure G¯ and analytic boundary and let μ be a positive measure carried by G¯ together with finitely many pure points outside G. We provide estimates on the norms of the monic polynomials of minimal norm in the space Lq(μ) for q>0. In case the norms converge to 0, we provide estimates on the rate of convergence, generalizing several previous results. Our most powerful result concerns measures μ that are perturbations of measures that are absolutely continuous with respect to the push-forward of a product measure near the boundary of the unit disk. Our results and methods also yield information about the strong asymptotics of the extremal polynomials and some information concerning Christoffel functions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 170, June 2013, Pages 172-197
Journal: Journal of Approximation Theory - Volume 170, June 2013, Pages 172-197
نویسندگان
Brian Simanek,