Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
-
Agata Bezubik
,
Jiří Hrivnák
Abstract
The common exponential functions whose exponents are the scalar products 〈λ,x〉, where x is a real variable and λ is an integer, admit two generalizations to any higher dimension, the symmetric and the antisymmetric ones [KLIMYK, A.—PATERA, J.: (Anti)symmetric multivariate exponential functions and corresponding Fourier transforms, J. Phys. A: Math. Theor. 40 (2007), 10473–10489]. Restriction in the paper to the three variables only allows us to work out many specific properties of the symmetric and antisymmetric functions useful in applications. Such are (i) the orthogonalities, both the continuous one and the discrete one on the 3D lattice of any density; (ii) corresponding discrete and continuous Fourier transforms; (iii) generating functions for the related polynomials in three variables, and others. Rapidly increasing precision of the interpolation with increasing density of the 3D lattice is shown in an example.
We gratefully acknowledge the support of this work by the Natural Sciences and Engineering Research Council of Canada and by the Doppler Institute of the Czech Technical University in Prague. JH is grateful for the hospitality extended to him at the Centre de recherches mathématiques, Université de Montréal. JP expresses his gratitude for the hospitality of the Doppler Institute. AB is grateful for the hospitality extended to her at Department of mathematics FNSPE CTU. SP acknowledges the support of SGS15/215/OHK4/3T/14, project of the Czech Technical University in Prague. JH gratefully acknowledges support by RVO68407700.
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© 2017 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- 10.1515/ms-2015-0200
- Zero-divisor graphs of lower dismantlable lattices I
- Some results on the intersection graph of submodules of a module
- Class number parities of compositum of quadratic function fields
- Examples of beurling prime systems
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Connection between multiplication theorem for Bernoulli polynomials and first factor
- On permutational invariance of the metric discrepancy results
- Evaluation of sums containing triple aerated generalized Fibonomial coefficients
- Linear algebraic proof of Wigner theorem and its consequences
- A note on groups with finite conjugacy classes of subnormal subgroups
- Groups with the same complex group algebras as some extensions of psl(2, pn)
- Klee-Phelps convex groupoids
- On analytic functions with generalized bounded Mocanu variation in conic domain with complex order
- Weak interpolation for the lipschitz class
- Generalized Padé approximants for plane condenser and distribution of points
- Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
- Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential
- Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem
- Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses
- On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term
- Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential
- Semi-equivelar maps on the torus and the Klein bottle with few vertices
- A problem considered by Friedlander & Iwaniec and the discrete Hardy-Littlewood method
