Parameter and q asymptotics of Lq$$ {\mathfrak{L}}_q $$‐norms of hypergeometric orthogonal polynomials
Sign Up to like & getrecommendations! Published in 2022 at "International Journal of Quantum Chemistry"
DOI: 10.1002/qua.27013
Abstract: . The three canonical families of the hypergeometric orthogonal polynomials (Hermite, Laguerre and Jacobi) control the physical wavefunctions of the bound stationary states of a great deal of quantum systems. The algebraic L q -norms… read more here.
Keywords: orthogonal polynomials; asymptotics mathfrak; norms hypergeometric; parameter asymptotics ... See more keywords
Three-Term Recurrence Relations for Systems of Clifford Algebra-Valued Orthogonal Polynomials
Sign Up to like & getrecommendations! Published in 2017 at "Advances in Applied Clifford Algebras"
DOI: 10.1007/s00006-015-0596-z
Abstract: Recently, systems of Clifford algebra-valued orthogonal polynomials have been studied from different points of view. We prove in this paper that for their building blocks there exist some three-term recurrence relations, similar to that for… read more here.
Keywords: valued orthogonal; clifford; clifford algebra; orthogonal polynomials ... See more keywords
Orthogonal Structure on a Wedge and on the Boundary of a Square
Sign Up to like & getrecommendations! Published in 2019 at "Foundations of Computational Mathematics"
DOI: 10.1007/s10208-018-9393-0
Abstract: Orthogonal polynomials with respect to a weight function defined on a wedge in the plane are studied. A basis of orthogonal polynomials is explicitly constructed for two large class of weight functions and the convergence… read more here.
Keywords: wedge boundary; orthogonal structure; boundary square; structure wedge ... See more keywords
A Class of Orthogonal Polynomials on the Boundary of an Ellipse
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Sciences"
DOI: 10.1007/s10958-019-04311-z
Abstract: We construct a class of polynomials of one complex variable that are pairwise orthogonal with some weight on the boundary of an ellipse. We prove that an arbitrary λ-holomorphic Hölder function defined in an ellipse… read more here.
Keywords: ellipse; class orthogonal; orthogonal polynomials; boundary ellipse ... See more keywords
RIMFRA: Rotation-invariant multi-spectral facial recognition approach by using orthogonal polynomials
Sign Up to like & getrecommendations! Published in 2019 at "Multimedia Tools and Applications"
DOI: 10.1007/s11042-019-07816-6
Abstract: This paper proposes a novel rotation-invariant multi-spectral facial recognition approach (RIMFRA) by using orthogonal polynomials. In the first step, a rotation, illumination and noise invariant local descriptor (RinLd) is proposed to represent the texture patterns… read more here.
Keywords: using orthogonal; blue; invariant multi; rotation ... See more keywords
Orthogonal Polynomials Related to $$_{g}$$g-Fractions with Missing Terms
Sign Up to like & getrecommendations! Published in 2017 at "Computational Methods and Function Theory"
DOI: 10.1007/s40315-017-0218-y
Abstract: The purpose of the present paper is to investigate some structural and qualitative aspects of two different perturbations of the parameters of g-fractions. In this context, the concept of gapg-fractions is introduced. While tail sequences… read more here.
Keywords: fractions missing; missing terms; related fractions; polynomials related ... See more keywords
On Finite Classes of Two-Variable Orthogonal Polynomials
Sign Up to like & getrecommendations! Published in 2019 at "Bulletin of the Iranian Mathematical Society"
DOI: 10.1007/s41980-019-00319-y
Abstract: The purpose of this paper is to introduce several finite sets of orthogonal polynomials in two variables, and investigate some general properties of them such as recurrence relations, generating functions, differential equations, and Rodrigues type… read more here.
Keywords: two variable; finite classes; variable orthogonal; orthogonal polynomials ... See more keywords
Asymptotic behavior of orthogonal polynomials without the Carleman condition
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Functional Analysis"
DOI: 10.1016/j.jfa.2020.108648
Abstract: Our goal is to find an asymptotic behavior as $n\to\infty$ of orthogonal polynomials $P_{n}(z)$ defined by the Jacobi recurrence coefficients $a_{n}, b_{n}$. We suppose that the off-diagonal coefficients $a_{n}$ grow so rapidly that the series… read more here.
Keywords: orthogonal polynomials; carleman condition; condition; polynomials without ... See more keywords
On the modifications of semi-classical orthogonal polynomials on nonuniform lattices
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DOI: 10.1016/j.jmaa.2016.06.041
Abstract: Abstract Semi classical orthogonal polynomials on nonuniform lattices with respect to a linear functional L are defined as polynomials ( P n ) where the degree of P n is exactly n, the P n… read more here.
Keywords: nonuniform lattices; classical orthogonal; linear functional; semi classical ... See more keywords
Moment representations of exceptional X1 orthogonal polynomials
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.05.037
Abstract: Abstract We generalize the representations of X 1 exceptional orthogonal polynomials through determinants of matrices that have certain adjusted moments as entries. We start out directly from the Darboux transformation, allowing for a universal perspective,… read more here.
Keywords: moment representations; exceptional orthogonal; adjusted moments; representations exceptional ... See more keywords
Orthogonal polynomials and the deformed Jordan plane
Sign Up to like & getrecommendations! Published in 2022 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125717
Abstract: We consider the unital associative algebra A with two generators X , Z obeying the defining relation [Z,X ] = Z + ∆. We construct irreducible tridiagonal representations of A. Depending on the value of… read more here.
Keywords: jordan plane; deformed jordan; orthogonal polynomials; polynomials deformed ... See more keywords