Wavelet-like transforms for admissible semi-groups; Inversion formulas for potentials and radon transforms

Ilham A. Aliev; Boris Rubin

doi:10.1007/s00041-005-4034-9

Wavelet-like transforms for admissible semi-groups; Inversion formulas for potentials and radon transforms

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

We introduce a family of wavelet-like transforms associated to certain admissible semigroups of operators acting on L_p-spaces, and prove the corresponding reproducing formula of Calderòn's type. The new transforms constitute a unified approach to inversion of a wide class of integral operators in analysis and applications. We illustrate the general theory by considering Riesz and Bessel potentials (associated to the ordinary and the generalized translation), and the k-plane Radon transform on ℝ ⁿ. 2005

Original language	English
Pages (from-to)	333-352
Number of pages	20
Journal	Journal of Fourier Analysis and Applications
Volume	11
Issue number	3
DOIs	https://doi.org/10.1007/s00041-005-4034-9
State	Published - Jun 2005

Keywords

Bessel potentials
Generalized translation
Inversion formulas
Radon transforms
Riesz potentials
Stronly continuous semigroups
Wavelet transforms

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10.1007/s00041-005-4034-9

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abstract = "We introduce a family of wavelet-like transforms associated to certain admissible semigroups of operators acting on Lp-spaces, and prove the corresponding reproducing formula of Calder{\`o}n's type. The new transforms constitute a unified approach to inversion of a wide class of integral operators in analysis and applications. We illustrate the general theory by considering Riesz and Bessel potentials (associated to the ordinary and the generalized translation), and the k-plane Radon transform on ℝ n. 2005",

keywords = "Bessel potentials, Generalized translation, Inversion formulas, Radon transforms, Riesz potentials, Stronly continuous semigroups, Wavelet transforms",

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T1 - Wavelet-like transforms for admissible semi-groups; Inversion formulas for potentials and radon transforms

AU - Aliev, Ilham A.

AU - Rubin, Boris

PY - 2005/6

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N2 - We introduce a family of wavelet-like transforms associated to certain admissible semigroups of operators acting on Lp-spaces, and prove the corresponding reproducing formula of Calderòn's type. The new transforms constitute a unified approach to inversion of a wide class of integral operators in analysis and applications. We illustrate the general theory by considering Riesz and Bessel potentials (associated to the ordinary and the generalized translation), and the k-plane Radon transform on ℝ n. 2005

AB - We introduce a family of wavelet-like transforms associated to certain admissible semigroups of operators acting on Lp-spaces, and prove the corresponding reproducing formula of Calderòn's type. The new transforms constitute a unified approach to inversion of a wide class of integral operators in analysis and applications. We illustrate the general theory by considering Riesz and Bessel potentials (associated to the ordinary and the generalized translation), and the k-plane Radon transform on ℝ n. 2005

KW - Bessel potentials

KW - Generalized translation

KW - Inversion formulas

KW - Radon transforms

KW - Riesz potentials

KW - Stronly continuous semigroups

KW - Wavelet transforms

UR - https://www.scopus.com/pages/publications/23944431861

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SN - 1069-5869

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SP - 333

EP - 352

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 3

ER -

Wavelet-like transforms for admissible semi-groups; Inversion formulas for potentials and radon transforms

Abstract

Keywords

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