ORTHOGONAL POLYNOMIALS ON SEVERAL INTERVALS VIA A POLYNOMIAL MAPPING
ORTHOGONAL POLYNOMIALS ON SEVERAL INTERVALS VIA A POLYNOMIAL MAPPING
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通过多项式映射计算多个区间上的正交多项式
DOI：
10.1090/s0002-9947-1988-0951620-6
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发表时间：
1988
影响因子：
1.3
通讯作者：
W. Assche
中科院分区：
文献类型：
--
作者：
J. Geronimo;W. Assche
从序列{pn{x；在Eo C（- 1,1）上，我们构造了一个新的正交多项式序列{p ' ' (x;fi)}，它在£= T~1(Eq) （T是TV次多项式）上，具有一个与no相关的正交测度(i)。如果Eo =(- 1,1)，则E = T_1（(-l,l)）通常由TV区间组成。我们给出了有关{pn(x;fi)}和{pn(x;fio)}的显式公式，并说明了这些正交多项式的三项递归公式中的递归系数是如何相互关联的。如果选择T作为第一类的切比雪夫多项式，那么就得到了筛选的正交多项式。
Starting from a sequence {pn{x; no)} of orthogonal polynomials with an orthogonality measure yurj supported on Eo C (—1,1), we construct a new sequence {p"(x;fi)} of orthogonal polynomials on£ = T~1(Eq) (T is a polynomial of degree TV) with an orthogonality measure (i that is related to no- If Eo = (—1,1), then E = T_1((-l,l)) will in general consist of TV intervals. We give explicit formulas relating {pn(x;fi)} and {pn(x;fio)} and show how the recurrence coefficients in the three-term recurrence formulas for these orthogonal polynomials are related. If one chooses T to be a Chebyshev polynomial of the first kind, then one gets sieved orthogonal polynomials.