Parabolic potentials and wavelet transforms with the generalized translation

Ilham A. Aliev; Boris Rubin

doi:10.4064/sm145-1-1

Parabolic potentials and wavelet transforms with the generalized translation

Ilham A. Aliev^*
, Boris Rubin

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

Parabolic wavelet transforms associated with the singular heat operators -Δγ+∂/∂t and I - Δγ + ∂/∂t, where Δγ = Σⁿ_k=1 ∂²/∂x²_k + (2γ/x_n)∂/∂x_n, are introduced. These transforms are defined in terms of the relevant generalized translation operator. An analogue of the Calderön reproducing formula is established. New inversion formulas are obtained for generalized parabolic potentials representing negative powers of the singular heat operators.

Original language	English
Pages (from-to)	1-16
Number of pages	16
Journal	Studia Mathematica
Volume	145
Issue number	1
DOIs	https://doi.org/10.4064/sm145-1-1
State	Published - 2001

Keywords

Calderón's reproducing formula
Generalized translation operator
Parabolic potentials
Parabolic wavelet transforms
Singular heat operators

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KW - Calderón's reproducing formula

KW - Generalized translation operator

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KW - Singular heat operators

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Parabolic potentials and wavelet transforms with the generalized translation

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Keywords

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