Parabolic potentials and wavelet transforms with the generalized translation

Ilham A. Aliev; Boris Rubin

Studia Mathematica, Tome 147 (2001), p. 1-16 / Harvested from The Polish Digital Mathematics Library

Résumé

Parabolic wavelet transforms associated with the singular heat operators $- Δ_{γ} + \partial / \partial t$ and $I - Δ_{γ} + \partial / \partial t$ , where $Δ_{γ} = \sum_{k = 1}^{n} \partial ² / \partial x ²_{k} + (2 γ / x ₙ) \partial / \partial x ₙ$ , 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.

Publié le : 2001-01-01

Zbl 0971.42030

EUDML-ID : urn:eudml:doc:285263

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     title = {Parabolic potentials and wavelet transforms with the generalized translation},
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     year = {2001},
     pages = {1-16},
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     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-1-1}
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Ilham A. Aliev; Boris Rubin. Parabolic potentials and wavelet transforms with the generalized translation. Studia Mathematica, Tome 147 (2001) pp. 1-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-1-1/