کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607725 1337880 2010 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On orthogonal polynomials obtained via polynomial mappings
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
On orthogonal polynomials obtained via polynomial mappings
چکیده انگلیسی

Let (pn)n(pn)n be a given monic orthogonal polynomial sequence (OPS) and kk a fixed positive integer number such that k≥2k≥2. We discuss conditions under which this OPS originates from a polynomial mapping in the following sense: to find another monic OPS (qn)n(qn)n and two polynomials πkπk and θmθm, with degrees kk and mm (resp.), with 0≤m≤k−10≤m≤k−1, such that pnk+m(x)=θm(x)qn(πk(x))(n=0,1,2,…). In this work we establish algebraic conditions for the existence of a polynomial mapping in the above sense. Under such conditions, when (pn)n(pn)n is orthogonal in the positive-definite sense, we consider the corresponding inverse problem, giving explicitly the orthogonality measure for the given OPS (pn)n(pn)n in terms of the orthogonality measure for the OPS (qn)n(qn)n. Some applications and examples are presented, recovering several known results in a unified way.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 162, Issue 12, December 2010, Pages 2243–2277
نویسندگان
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