Multivariate Fourier Series Over a Class of Non Tensor-Product Partition Domains
Jiachang Sun 11 Parallel Computing Division, Institute of Software, Chinese Academy of Sciences, Beijing 100080, China
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.
Key words: Multivariate Fourier methods; Non tensor-product partitions; Multivariate Fourier series.