کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4638506 | 1632007 | 2015 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Orthogonal polynomials for Minkowski's question mark function
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
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چکیده انگلیسی
Hermann Minkowski introduced a function in 1904 which maps quadratic irrational numbers to rational numbers and this function is now known as Minkowski's question mark function since Minkowski used the notation ?(x). This function is a distribution function on [0,1] which defines a singular continuous measure with support [0,1]. Our interest is in the (monic) orthogonal polynomials (Pn)nâN for the Minkowski measure and in particular in the behavior of the recurrence coefficients of the three term recurrence relation. We will give some numerical experiments using the discretized Stieltjes-Gautschi method with a discrete measure supported on the Minkowski sequence. We also explain how one can compute the moments of the Minkowski measure and compute the recurrence coefficients using the Chebyshev algorithm.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 284, 15 August 2015, Pages 171-183
Journal: Journal of Computational and Applied Mathematics - Volume 284, 15 August 2015, Pages 171-183
نویسندگان
Zoé Dresse, Walter Van Assche,