152 research outputs found
Three variable exponential functions of the alternating group
New class of special functions of three real variables, based on the
alternating subgroup of the permutation group , is studied. These
functions are used for Fourier-like expansion of digital data given on lattice
of any density and general position. Such functions have only trivial analogs
in one and two variables; a connection to the functions of is shown.
Continuous interpolation of the three dimensional data is studied and
exemplified.Comment: 10 pages, 3 figure
Two-dimensional symmetric and antisymmetric generalizations of exponential and cosine functions
Properties of the four families of recently introduced special functions of
two real variables, denoted here by , and , are studied. The
superscripts and refer to the symmetric and antisymmetric functions
respectively. The functions are considered in all details required for their
exploitation in Fourier expansions of digital data, sampled on square grids of
any density and for general position of the grid in the real plane relative to
the lattice defined by the underlying group theory. Quality of continuous
interpolation, resulting from the discrete expansions, is studied, exemplified
and compared for some model functions.Comment: 22 pages, 10 figure
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