Parabolic potentials and wavelet transforms with the generalized translation

Ilham A. Aliev, and Boris Rubin. "Parabolic potentials and wavelet transforms with the generalized translation." Studia Mathematica 145.1 (2001): 1-16. <http://eudml.org/doc/285263>.

@article{IlhamA2001,
abstract = {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.},
author = {Ilham A. Aliev, Boris Rubin},
journal = {Studia Mathematica},
keywords = {parabolic wavelet transforms; parabolic potentials; generalized translation operator; singular heat operators; Calderón’s reproducing formula},
language = {eng},
number = {1},
pages = {1-16},
title = {Parabolic potentials and wavelet transforms with the generalized translation},
url = {http://eudml.org/doc/285263},
volume = {145},
year = {2001},
}

TY - JOUR
AU - Ilham A. Aliev
AU - Boris Rubin
TI - Parabolic potentials and wavelet transforms with the generalized translation
JO - Studia Mathematica
PY - 2001
VL - 145
IS - 1
SP - 1
EP - 16
AB - 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.
LA - eng
KW - parabolic wavelet transforms; parabolic potentials; generalized translation operator; singular heat operators; Calderón’s reproducing formula
UR - http://eudml.org/doc/285263
ER -