Matrix biorthogonal polynomials on the real line: Geronimus 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...
متن کاملDuality, Biorthogonal Polynomials and Multi–Matrix Models
The statistical distribution of eigenvalues of pairs of coupled random matrices can be expressed in terms of integral kernels having a generalized Christoffel–Darboux form constructed from sequences of biorthogonal polynomials. For measures involving exponentials of a pair of polynomials V1, V2 in two different variables, these kernels may be expressed in terms of finite dimensional “windows” s...
متن کاملOld and New Geronimus Type Identities for Real Orthogonal Polynomials
Let be a positive measure on the real line, with orthogonal polynomials fpng and leading coe¢ cients f ng. The Geronimus type identity 1 jIm zj Z 1 1 P (t) jzpn (t) pn 1 (t)j dt = n 1 n Z P (t) d (t) ; valid for all polynomials P of degree 2n 2 has known analogues within the theory of orthogonal rational functions, though apparently unknown in the theory of orthogonal polynomials. We present ne...
متن کاملCmv Biorthogonal Laurent Polynomials: Christoffel Formulas for Christoffel and Geronimus Perturbations
Quasidefinite sesquilinear forms for Laurent polynomials in the complex plane and corresponding CMV biorthogonal Laurent polynomial families are studied. Bivariate linear functionals encompass large families of orthogonalities like Sobolev and discrete Sobolev types. Two possible Christoffel transformations of these linear functionals are discussed. Either the linear functionals are multiplied ...
متن کاملApplications of New Geronimus Type Identities for Real Orthogonal Polynomials
Let be a positive measure on the real line, with associated orthogonal polynomials fpng. Let Im a 6= 0. Then there is an explicit constant cn such that for all polynomials P of degree at most 2n 2, cn Z 1 1 P (t) jpn (a) pn 1 (t) pn 1 (a) pn (t)j dt = Z P d : In this paper, we provide a self-contained proof of the identity. Moreover, we apply the formula to deduce a weak convergence result, a d...
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: Bulletin of Mathematical Sciences
سال: 2019
ISSN: 1664-3607,1664-3615
DOI: 10.1142/s1664360719500073