Maximal estimates for a generalized spherical mean Radon transform acting on radial functions
نویسندگان
چکیده
منابع مشابه
Spherical Maximal Operators on Radial Functions
where dσ is the rotationally invariant measure on Sd−1, normalized such that σ(Sd−1) = 1. Stein [5] showed that limt→0Atf(x) = f(x) almost everywhere, provided f ∈ L(R), p > d/(d − 1) and d ≥ 3. Later Bourgain [1] extended this result to the case d = 2. If p ≤ d/(d − 1) then pointwise convergence fails. However if {tj}j=1 is a fixed sequence converging to 0 then pointwise convergence may hold f...
متن کاملRange Descriptions for the Spherical Mean Radon Transform. I. Functions Supported in A
The transform considered in the paper averages a function supported in a ball in Rn over all spheres centered at the boundary of the ball. This Radon type transform arises in several contemporary applications, e.g. in thermoacoustic tomography and sonar and radar imaging. Range descriptions for such transforms are important in all these areas, for instance when dealing with incomplete data, err...
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Abstract We derive explicit formulae for the reconstruction of a function from its integrals over a family of spheres, or for the inversion of the spherical mean Radon transform. Such formulae are important for problems of thermoand photo-acoustic tomography. A closed-form inversion formula of a filtrationbackprojection type is found for the case when the centres of the integration spheres lie ...
متن کاملRange descriptions for the spherical mean Radon transform ∗
The transform considered in the paper averages a function supported in a ball in Rn over all spheres centered at the boundary of the ball. This Radon type transform arises in several contemporary applications, e.g. in thermoacoustic tomography and sonar and radar imaging. Range descriptions for such transforms are important in all these areas, for instance when dealing with incomplete data, err...
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Abstract In this paper we refer to the reconstruction formulas given in Andersson’s On the determination of a function from spherical averages, which are often used in applications such as SAR1 and SONAR2. We demonstrate that the first one of these formulas does not converge given physically reasonable assumptions. An alternative is proposed and it is shown that the second reconstruction formul...
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ژورنال
عنوان ژورنال: Annali di Matematica Pura ed Applicata (1923 -)
سال: 2019
ISSN: 0373-3114,1618-1891
DOI: 10.1007/s10231-019-00933-x