Biorthogonal polynomials and zero-mapping transformations
نویسندگان
چکیده
منابع مشابه
Biorthogonal polynomials and zero-mapping transformations
The authors have presented in [6] a technique to generate transformations T of the set Pn of nth degree polynomials to itself such that if p ∈ Pn has all its zeros in (c, d) then T {p} has all its zeros in (a, b), where (a, b) and (c, d) are given real intervals. The technique rests upon the derivation of an explicit form of biorthogonal polynomials whose Borel measure is strictly sign consiste...
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Let ψ : [0, 1] → R be a strictly increasing continuous function. Let Pn be a polynomial of degree n determined by the biorthogonality conditions ∫ 1 0 Pn (x)ψ (x) j dx = 0, j = 0, 1, . . . , n− 1. We study the distribution of zeros of Pn as n → ∞, and related potential theory.
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We analyze polynomials Pn that are biorthogonal to exponentials {e−σn,j }j=1, in the sense that ∫ ∞ 0 Pn(x)e −σn,j x dx = 0, 1 ≤ j ≤ n. Here α >−1. We show that the zero distribution of Pn as n→∞ is closely related to that of the associated exponent polynomial Qn(y)= n ∏ j=1 (y + 1/σn,j )= n ∑ j=0 qn,j y j . More precisely, we show that the zero counting measures of {Pn(−4nx)}∞n=1 converge weak...
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Let α > 0 and ψ (x) = x. Let Sn,α be a polynomial of degree n determined by the biorthogonality conditions Z 1 0 Sn,αψ j = 0, j = 0, 1, . . . , n− 1. We explicitly determine Sn,α and discuss some other properties, including their zero distribution. We also discuss their relation to the Sidi polynomials. §
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1997
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(96)00225-8