Abstract:Let Q be the quaternion Heisenberg group, and let P be the affine automorphism group of Q. We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of P on L 2 (Q). A class of radial wavelets is constructed. The inverse wavelet transform is simplified by using radial wavelets. Then we investigate the Radon transform on Q. A Semyanistri-Lizorkin space is introduced, on which the Radon transform is a bijection. We deal with the Radon transform on Q … Show more
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