Twodimensional symmetric and antisymmetric generalizations of sine functions
Abstract
The properties of twodimensional generalizations of sine functions that are symmetric or antisymmetric with respect to permutations of their two variables are described. It is shown that the functions are orthogonal when integrated over a finite region F of the real Euclidean space, and that they are discretely orthogonal when summed up over a lattice of any density in F. The decomposability of the products of functions into their sums is shown by explicitly decomposing products of all types. The formalism is set up for Fourierlike expansions of the digital data over twodimensional lattices in F. Analogs of the common cosine transforms of types IIV are described. Continuous interpolation of the digital data is studied.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 July 2010
 DOI:
 10.1063/1.3430567
 arXiv:
 arXiv:0912.0241
 Bibcode:
 2010JMP....51g3509H
 Keywords:

 functional analysis;
 02.30.Sa;
 Functional analysis;
 Mathematical Physics
 EPrint:
 12 pages, 5 figures