A Combinatorial Representation with Schroder Paths of Biorthogonality of Laurent Biorthogonal Polynomials
نویسنده
چکیده
Combinatorial representation in terms of Schröder paths and other weighted plane paths are given of Laurent biorthogonal polynomials (LBPs) and a linear functional with which LBPs have orthogonality and biorthogonality. Particularly, it is clarified that quantities to which LBPs are mapped by the corresponding linear functional can be evaluated by enumerating certain kinds of Schröder paths, which imply orthogonality and biorthogonality of LBPs.
منابع مشابه
A Combinatorial Derivation with Schroder Paths of a Determinant Representation of Laurent Biorthogonal Polynomials
A combinatorial proof in terms of Schröder paths and other weighted plane paths is given for a determinant representation of Laurent biorthogonal polynomials (LBPs) and that of coefficients of their three-term recurrence equation. In this process, it is clarified that Toeplitz determinants of the moments of LBPs and their minors can be evaluated by enumerating certain kinds of configurations of...
متن کاملSome Explicit Biorthogonal Polynomials
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. §
متن کاملOrthogonal basic hypergeometric Laurent polynomials
The Askey-Wilson polynomials are orthogonal polynomials in x = cos θ, which are given as a terminating 4φ3 basic hypergeometric series. The non-symmetric AskeyWilson polynomials are Laurent polynomials in z = eiθ, which are given as a sum of two terminating 4φ3’s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single 4φ3’s which are Laurent polynomials in...
متن کاملNonstationary Biorthogonal Wavelet Systems Based on Exponential B-Splines
and Applied Analysis 3 Wj and W̃j of Vj and Ṽj , respectively, satisfying Vj 1 Vj ̇Wj , Wj ⊥ Ṽj and Ṽj 1 Ṽj ̇W̃j , W̃j ⊥ Vj . The corresponding biorthogonal wavelets are given by ψj ∑ n∈Z −1 ã j 1−nφj 1 2 · −n , ψ̃j ∑ n∈Z −1 a j 1−nφ̃j 1 2 · −n . 1.4 A generalization of the biorthogonal wavelets of Cohen-Daubechies-Feuveau 1 was introduced that was based on exponential B-splines 12 . By generalizing...
متن کاملElliptic Integrable Systems Padé Interpolation Table and Biorthogonal Rational Functions
We study recurrence relations and biorthogonality properties for polynomials and rational functions in the problem of the Padé interpolation in the usual scheme and in the scheme with prescribed poles and zeros. The main result is deriving explicit orthogonality and biorthogonality relations for polynomials and rational functions in both schemes. We show that the simplest linear restrictions in...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 14 شماره
صفحات -
تاریخ انتشار 2007