Discretization of four types of Weyl group orbit functions

21st International Conference on Integrable Systems and Quantum Symmetries

Hrivnák, Jirí^1

Department of Physics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Brehová 7, 115 19 Prague 1, Czech Republic^1

关键词: Continuous interpolations;    Discrete cosines;    Discretizations;    Finite set;    L functions;    Sine transforms;    Special functions;    Spectral methods;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012021/pdf
DOI  :  10.1088/1742-6596/474/1/012021

来源: IOP

【 摘 要 】

The discrete Fourier calculus of the four families of special functions, called C-, S-, Ss- and Sl-functions, is summarized. Functions from each of the four families of special functions are discretely orthogonal over a certain finite set of points. The generalizations of discrete cosine and sine transforms of one variable - the discrete Ss- and Sl-transforms of the group F4- are considered in detail required for their exploitation in discrete Fourier spectral methods. The continuous interpolations, induced by the discrete expansions, are presented.