کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9518813 1346127 2005 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On polynomials orthogonal to all powers of a given polynomial on a segment
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
On polynomials orthogonal to all powers of a given polynomial on a segment
چکیده انگلیسی
In this paper we investigate the following “polynomial moment problem”: for a given complex polynomial P(z) and distinct a,b∈C to describe polynomials q(z) orthogonal to all powers of P(z) on [a,b]. We show that for given P(z), q(z) the condition that q(z) is orthogonal to all powers of P(z) is equivalent to the condition that branches of the algebraic function Q(P−1(z)), where Q(z)=∫q(z)dz, satisfy a certain system of linear equations over Z. On this base we provide the solution of the polynomial moment problem for wide classes of polynomials. In particular, we give the complete solution for polynomials of degree less than 10.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Bulletin des Sciences Mathématiques - Volume 129, Issue 9, October 2005, Pages 749-774
نویسندگان
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