Discrete Fourier analysis with lattices on planar domains

Authors:
Huiyuan Li;Jiachang Sun;Yuan Xu
Affiliations:
Institute of Software, Chinese Academy of Sciences, Beijing, China 100190;Institute of Software, Chinese Academy of Sciences, Beijing, China 100190;Department of Mathematics, University of Oregon, Eugene, USA 97403-1222
Venue:
Numerical Algorithms
Year:
2010

Citing 4
Cited 0

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Abstract

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 ${{\mathbb R}}^2$ and several new results on cubature and interpolation by trigonometric, as well as algebraic, polynomials are obtained.