Discrete Fourier analysis with lattices on planar domains

Details Discrete Fourier analysis with lattices on planar domains Discrete Fourier analysis with lattices on planar domains

2009-10-28

arxiv.org/abs/0910.5286v1

Mathematics

Numerical Analysis

Scientific paper

A discrete Fourier analysis associated with translation lattices is developed recently by the authors. It permits two lattices, one determining the integral domain and the other determining the family of exponential functions. Possible choices of lattices are discussed in the case of lattices that tile $\RR^2$ and several new results on cubature and interpolation by trigonometric, as well as algebraic, polynomials are obtained.

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