(Anti)symmetric multivariate exponential functions and corresponding Fourier transforms

Abstract

We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are eigenfunctions of the Laplace operator on corresponding fundamental domains satisfying certain boundary conditions. To symmetric and antisymmetric multivariate exponential functions there correspond Fourier transforms. There are three types of such Fourier transforms: expansions into corresponding Fourier series, integral Fourier transforms, and multivariate finite Fourier transforms. Eigenfunctions of the integral Fourier transforms are found.

18 pages, no figeres

References in corpus (5)

• Antisymmetric Orbit Functions
• E-Orbit Functions
• Orthogonality within the Families of C-, S-, and E-Functions of Any Compact Semisimple Lie Group
• Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization
• Fourier transform method for imaging atmospheric Cherenkov telescopes

Cited by in corpus (10)

• E-Orbit Functions
• (Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
• Discrete Fourier analysis on fundamental domain of $A_d$ lattice and on simplex in $d$-variables
• Two-dimensional symmetric and antisymmetric generalizations of exponential and cosine functions
• Discrete Fourier transform associated with generalized Schur polynomials
• Two dimensional symmetric and antisymmetric generalizations of sine functions
• Three dimensional C-, S- and E-transforms
• Four families of Weyl group orbit functions of B_3 and C_3
• Orbit functions of SU(n) and Chebyshev polynomials
• Three variable exponential functions of the alternating group