Parabolic potentials and wavelet transforms with the generalized translation

Ilham A. Aliev¹ ; Boris Rubin²

¹Department of Mathematics Akdeniz University 07058 Antalya, Turkey
²Institute of Mathematics The Hebrew University 91904 Jerusalem, Israel

Studia Mathematica, Tome 145 (2001) no. 1, pp. 1-16

Résumé

Parabolic wavelet transforms associated with the singular heat operators $-{\mit \Delta }_{\gamma }+{\partial /\partial t}$ and $I-{\mit \Delta }_{\gamma }+{\partial /\partial t}$, where ${\mit \Delta }_{\gamma }=\sum _{k=1}^{n} {\partial ^2/\partial x_{k}^{2}}+({2\gamma /x_{n}}) {\partial /\partial x_{n}}$, are introduced. These transforms are defined in terms of the relevant generalized translation operator. An analogue of the Calderón reproducing formula is established. New inversion formulas are obtained for generalized parabolic potentials representing negative powers of the singular heat operators.

Détail

DOI : 10.4064/sm145-1-1

Keywords: parabolic wavelet transforms associated singular heat operators mit delta gamma partial partial i mit delta gamma partial partial where mit delta gamma sum partial partial gamma partial partial introduced these transforms defined terms relevant generalized translation operator analogue calder reproducing formula established inversion formulas obtained generalized parabolic potentials representing negative powers singular heat operators