کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8898465 | 1631385 | 2018 | 30 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Symmetric contours and convergent interpolation
ترجمه فارسی عنوان
خطوط متقارن و درونیابی همگرا
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
چکیده انگلیسی
The essence of Stahl-Gonchar-Rakhmanov theory of symmetric contours as applied to the multipoint Padé approximants is the fact that given a germ of an algebraic function and a sequence of rational interpolants with free poles of the germ, if there exists a contour that is “symmetric” with respect to the interpolation scheme, does not separate the plane, and in the complement of which the germ has a single-valued continuation with non-identically zero jump across the contour, then the interpolants converge to that continuation in logarithmic capacity in the complement of the contour. The existence of such a contour is not guaranteed. In this work we do construct a class of pairs interpolation scheme/symmetric contour with the help of hyperelliptic Riemann surfaces (following the ideas of Nuttall and Singh, 1977; Baratchart and Yattselev, 2009). We consider rational interpolants with free poles of Cauchy transforms of non-vanishing complex densities on such contours under mild smoothness assumptions on the density. We utilize âÌ-extension of the Riemann-Hilbert technique to obtain formulae of strong asymptotics for the error of interpolation.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 225, January 2018, Pages 76-105
Journal: Journal of Approximation Theory - Volume 225, January 2018, Pages 76-105
نویسندگان
Maxim L. Yattselev,