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The aim of this paper is to obtain necessary and sufficient conditions forthe orthonormality of wavelet system arising out of left translations andnonisotropic dilations on the Heisenberg group $\mathbb{H}$. A similar problemis also discussed for the twisted wavelet system on $\mathbb{C}$.

Orthonormality of wavelet system on the Heisenberg group and twisted wavelet system on $\mathbb{C}$