Continuous Wavelet Transform on the One-sheeted Hyperboloid

A. Askari Hemmat, Z. Yazdani Fard


In this work a constructive theory for the CWT on the one-sheeted hyperboloid, $H^{1,1}$, has been developed. The construction is based on the notion of convolution on this manifold. We defined the affine transformations on the $H^{1,1}$.\ These are of two types: motions and dilations. We defined the CWT on $H^{1,1}$ through a $H^{1,1}$-convolution and derived the corresponding admissibility condition.


Continuous wavelet transform; Fourier-Helgason transform; one-sheeted hyperboloid

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eISSN 0975-8607; pISSN 0976-5905