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Parabolic potentials and wavelet transforms with the generalized translation

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Aliev I., Rubin B.

Studia Mathematica

2001

tom 145

nr 1

1-16

Parabolic wavelet transforms associated with the singular heat operators $- Δ_{γ} + ∂/∂t$ and $I - Δ_{γ} + ∂/∂t$, where $Δ_{γ} = ∑_{k=1}^{n} {∂²/∂x²_{k}} + (2γ/xₙ) ∂/∂xₙ$, 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.

Ograniczanie wyników

1 Studia Mathematica

1 Aliev I.

1 Rubin B.

1 2001

Wyniki wyszukiwania

Parabolic potentials and wavelet transforms with the generalized translation