Summary
Index transforms ofm-dimensional arrays inton-dimensional arrays play a significant role in many fast algorithms of multivariate discrete Fourier transforms (DFT's) and cyclic convolutions. The computation ofm-dimensional “long” DFT's or convolutions can be transfered to the parallel computation ofn-dimensional “short” DFT's or convolutions (n>m). In this paper, the nature of index transforms is explored using group-theoretical ideas. We solve the open problems concerning index transforms posed recently by Hekrdla [5, 6].
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