Asymptotic of Cauchy Biorthogonal Polynomials
نویسندگان
چکیده
منابع مشابه
Cauchy biorthogonal polynomials
The paper investigates the properties of certain biorthogonal polynomials appearing in a specific simultaneous Hermite–Padé approximation scheme. Associated with any totally positive kernel and a pair of positive measures on the positive axis we define biorthogonal polynomials and prove that their zeros are simple and positive. We then specialize the kernel to the Cauchy kernel 1 x+y and show t...
متن کاملPeakons and Cauchy Biorthogonal Polynomials
Peakons are non-smooth soliton solutions appearing in certain nonlinear partial differential equations, most notably the Camassa-Holm equation and the Degasperis-Procesi equation. In the latter case the construction of peakons leads to a new class of biorthogonal polynomials. The present paper is the first in the series of papers aimed to establish a general framework in which to study such pol...
متن کاملStrong asymptotics for Cauchy biorthogonal polynomials
where U, V are scalar functions defined on R. The model was termed the Cauchy matrix model because of the shape of the coupling term. Similarly to the case of the Hermitean one-matrix models for which the spectral statistics is expressible in terms of appropriate orthogonal polynomials [3], this two-matrix model is solvable with the help of a new family of biorthogonal polynomials named the Cau...
متن کاملAsymptotic zero distribution of biorthogonal polynomials
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.
متن کاملCubic string boundary value problems and Cauchy biorthogonal polynomials
Cauchy Biorthogonal Polynomials appear in the study of special solutions to the dispersive nonlinear partial differential equation called the Degasperis-Procesi (DP) equation, as well as in certain two-matrix random matrix models. Another context in which such biorthogonal polynomials play a role is the cubic string; a third order ODE boundary value problem −f ′′′ = zgf which is a generalizatio...
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: Mediterranean Journal of Mathematics
سال: 2019
ISSN: 1660-5446,1660-5454
DOI: 10.1007/s00009-019-1455-2