Volume 21, Issue 1
Multivariate Fourier Series Over a Class of Non Tensor-Product Partition Domains

Jiachang Sun

J. Comp. Math., 21 (2003), pp. 53-62

Published online: 2003-02

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  • Abstract

This paper finds a way to extend the well-known Fourier methods, to so-called n+1 directions partition domains in n-dimension. In particular, in 2-D and 3-D cases, we study Fourier methods over 3-direction parallel hexagon partitions and 4-direction parallel parallelogram dodecahedron partitions, respectively. It has pointed that, the most concepts and results of Fourier methods on tensor-product case, such as periodicity, orthogonality of Fourier basis system, partial sum of Fourier siries and its approximation behavior, can be moved on the new non tensor-product partition case.

  • Keywords

Multivariate Fourier methods Non tensor-product partitions Multivariate Fourier series

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@Article{JCM-21-53, author = {}, title = {Multivariate Fourier Series Over a Class of Non Tensor-Product Partition Domains}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {1}, pages = {53--62}, abstract = { This paper finds a way to extend the well-known Fourier methods, to so-called n+1 directions partition domains in n-dimension. In particular, in 2-D and 3-D cases, we study Fourier methods over 3-direction parallel hexagon partitions and 4-direction parallel parallelogram dodecahedron partitions, respectively. It has pointed that, the most concepts and results of Fourier methods on tensor-product case, such as periodicity, orthogonality of Fourier basis system, partial sum of Fourier siries and its approximation behavior, can be moved on the new non tensor-product partition case. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10282.html} }
TY - JOUR T1 - Multivariate Fourier Series Over a Class of Non Tensor-Product Partition Domains JO - Journal of Computational Mathematics VL - 1 SP - 53 EP - 62 PY - 2003 DA - 2003/02 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10282.html KW - Multivariate Fourier methods KW - Non tensor-product partitions KW - Multivariate Fourier series AB - This paper finds a way to extend the well-known Fourier methods, to so-called n+1 directions partition domains in n-dimension. In particular, in 2-D and 3-D cases, we study Fourier methods over 3-direction parallel hexagon partitions and 4-direction parallel parallelogram dodecahedron partitions, respectively. It has pointed that, the most concepts and results of Fourier methods on tensor-product case, such as periodicity, orthogonality of Fourier basis system, partial sum of Fourier siries and its approximation behavior, can be moved on the new non tensor-product partition case.
Jiachang Sun. (1970). Multivariate Fourier Series Over a Class of Non Tensor-Product Partition Domains. Journal of Computational Mathematics. 21 (1). 53-62. doi:
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