کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9500690 1337935 2005 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the maximum value of Jacobi polynomials
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
On the maximum value of Jacobi polynomials
چکیده انگلیسی
A remarkable inequality, with utterly explicit constants, established by Erdélyi, Magnus, and Nevai, states that for α⩾β>-12, the orthonormal Jacobi polynomials Pk(α,β)(x) satisfymax|x|⩽1(1-x)α+1/2(1+x)β+1/2Pk(α,β)(x)2=O(α)[Erdélyi et al., Generalized Jacobi weights, Christoffel functions, and Jacobi polynomials, SIAM J. Math. Anal. 25 (1994), 602-614]. They conjectured that the real order of the maximum is O(α1/2). Here we will make half a way towards this conjecture by proving a new inequality which improves their result by a factor of order (1α+1k)-1/3. We also confirm the conjecture, even in a stronger form, in some limiting cases.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 136, Issue 1, September 2005, Pages 1-20
نویسندگان
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