Relative growth of linear iterations and orthogonal polynomials on several intervals
نویسندگان
چکیده
منابع مشابه
Zeros of Polynomials Orthogonal on Several Intervals
Let a1 < a2 < . . . < a2l, Ej = [a2j−1, a2j ], put E = ⋃l j=1 Ej and H(x) = ∏2l j=1(x − aj). Furthermore let pn(x) = x + . . . be the polynomial of degree n orthogonal on E with respect to a weight function of the form w/ √ −H with square root singularities at the boundary points of E and w ∈ C(E). We study and answer the following questions: how many zeros has pn in the interval Ej , j ∈ {1, ....
متن کاملOn Generating Polynomials Which Are Orthogonal over Several Intervals
We consider the problem of generating the recursion coefficients of orthogonal polynomials for a given weight function. The weight function is assumed to be the weighted sum of weight functions, each supported on its own interval. Some of these intervals may coincide, overlap or are contiguous. We discuss three algorithms. Two of them are based on modified moments, whereas the other is based on...
متن کاملOrthogonal Polynomials on Several Intervals via a Polynomial Mapping
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 rel...
متن کاملOrthogonal polynomials on several intervals: Accumulation points of recurrence coefficients and of zeros
Let E = ∪j=1[a2j−1, a2j ], a1 < a2 < ... < a2l, l ≥ 2 and set ω(∞) = (ω1(∞), ..., ωl−1(∞)), where ωj(∞) is the harmonic measure of [a2j−1, a2j ] at infinity. Let μ be a measure which is on E absolutely continuous and satisfies Szegő’s-condition and has at most a finite number of point measures outside E, and denote by (Pn) and (Qn) the orthonormal polynomials and their associated Weyl solutions...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1993
ISSN: 0024-3795
DOI: 10.1016/0024-3795(93)90287-x