Orthogonal Polynomials on Several Intervals via a Polynomial Mapping
نویسندگان
چکیده
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 noIf 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.
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