Results 1 to 10 of about 2,254 (120)
A difference-integral representation of Koornwinder polynomials
, 2004 We construct new families of (q-) difference and (contour) integral operators having nice actions on Koornwinder's multivariate orthogonal polynomials.
Eric M. Rains
core +8 more sources
Quadratic transformations of Macdonald and Koornwinder polynomials [PDF]
, 2006 When one expands a Schur function in terms of the irreducible characters of the symplectic (or orthogonal) group, the coefficient of the trivial character is 0 unless the indexing partition has an appropriate form.
Eric M. Rains, Monica Vazirani
core +7 more sources
Representations for parameter derivatives of some Koornwinder polynomials in two variables
Journal of the Egyptian Mathematical Society, 2016 In this paper, we give the parameter derivative representations in the form of ∂Pn,k(λ;x,y)∂λ=∑m=0n−1∑j=0mdn,j,mPm,j(λ;x,y)+∑j=0ken,j,kPn,j(λ;x,y) for some Koornwinder polynomials where λ is a parameter and 0 ≤ k ≤ n; n=0,1,2,… and present orthogonality ...
Rabia Aktaş
doaj +4 more sources
Boundary Interactions for the Semi-Infinite q-Boson System and Hyperoctahedral Hall-Littlewood Polynomials [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2013 We present a semi-infinite q-boson system endowed with a four-parameter boundary interaction. The n-particle Hamiltonian is diagonalized by generalized Hall-Littlewood polynomials with hyperoctahedral symmetry that arise as a degeneration of the ...
Jan Felipe van Diejen, Erdal Emsiz
doaj +3 more sources
Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements. [PDF]
Biomed Res Int, 2015 We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics.
Cuccuru G +3 more
europepmc +2 more sources
Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2009 A unified approach is given to kernel functions which intertwine Ruijsenaars difference operators of type A and of type BC. As an application of the trigonometric cases, new explicit formulas for Koornwinder polynomials attached to single columns and ...
Yasushi Komori +2 more
doaj +5 more sources
Sobolev‐orthogonal systems with tridiagonal skew‐Hermitian differentiation matrices
Studies in Applied Mathematics, Volume 150, Issue 2, Page 420-447, February 2023., 2023 Abstract We introduce and develop a theory of orthogonality with respect to Sobolev inner products on the real line for sequences of functions with a tridiagonal, skew‐Hermitian differentiation matrix. While a theory of such L2 ‐orthogonal systems is well established, Sobolev orthogonality requires new concepts and their analysis.
Arieh Iserles, Marcus Webb
wiley +1 more source
Bivariate Generalized Shifted Gegenbauer Orthogonal System
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 For K0, K1 ≥ 0, λ > −(1/2), we examine Cr∗λ,K0,K1x, generalized shifted Gegenbauer orthogonal polynomials, with reference to the weight Wλ,K0,K1x=2λΓ2λ/Γλ+12/2x−x2λ−12/Ix∈0,1dx+K0δ0+K1δ1, where the indicator function is denoted by Ix∈0,1 and δx indicates the Dirac δ−measure.
Mohammad A. Alqudah +3 more
wiley +1 more source
A new family of orthogonal polynomials in three variables
Journal of Inequalities and Applications, 2020 In this paper we introduce a six-parameter generalization of the four-parameter three-variable polynomials on the simplex and we investigate the properties of these polynomials.
Rabia Aktaş +2 more
doaj +1 more source
Okounkov's BC-type interpolation Macdonald polynomials and their q=1 limit [PDF]
, 2015 This paper surveys eight classes of polynomials associated with $A$-type and $BC$-type root systems: Jack, Jacobi, Macdonald and Koornwinder polynomials and interpolation (or shifted) Jack and Macdonald polynomials and their $BC$-type extensions.
Koornwinder, Tom H.
core +7 more sources