Abstract.
Wavelet–type transform associated with singular Laplace–Bessel differential operator \(\Delta _\nu = \sum\limits_{k = 1}^n {\frac{{\partial ^2 }} {{\partial x_k^2 }}} + \frac{{2\nu}} {{x_n }}\frac{\partial } {{\partial x_n }}\) is introduced and the relevant Calderón–type reproducing formula is established. Representations of the generalized Bessel potentials \((E - \Delta _\nu )^{ - \alpha /2} f,\quad (Re \alpha > 0)\) and their inverses via the wavelet–type transform are obtained.
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Aliev, I.A., Eryigit, M. Wavelet-type Transform and Bessel Potentials Associated with the Generalized Translation. Integr. equ. oper. theory 51, 303–317 (2005). https://doi.org/10.1007/s00020-004-1333-5
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DOI: https://doi.org/10.1007/s00020-004-1333-5