A problem of integral geometry for a family of curves with incomplete data

Аниконов, Д. С.; Konovalova, D. S.

doi:10.1134/s1064562415050026

Cited by 3 publications

(2 citation statements)

References 5 publications

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“…Theorem 2 If at the contact point z (i) ∈ ∂G (i) 0 V i (z (i) , z (i) ) ̸ = 0 and functions v 1 , v 2 have non-zero jumps at the points z (1) and z (2) , respectively , then from the match (1) , which contradicts the condition of the theorem. That's why z (1) ∈ ∂G…”

Section: Statement and Study Of The Problemmentioning

confidence: 94%

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A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform

Anikonov,

Kazantsev,

Konovalova

2023

Journal of Inverse and Ill-Posed Problems

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We study the problem of the integral geometry, in which the functions are integrated over hyperplanes in the n-dimensional Euclidean space, n = 2 ⁢ m + 1 {n=2m+1} . The integrand is the product of a function of n variables called the density and weight function depending on 2 ⁢ n {2n} variables. Such an integration is called here the weighted Radon transform, which coincides with the classical one if the weight function is equal to one. It is proved the uniqueness for the problem of determination of the surface on which the integrand is discontinuous.

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Section: Statement and Study Of The Problemmentioning

confidence: 94%

“…The present work is a continuation previous research of the authors in the field of the integral geometry [1], [2], [3]. Without claiming to be a complete review of the topic, we point to the works of the classics of this field, such as J. Radon [7], R. Courant [4], F. John [8], and M. Gelfand [6].…”

Section: Introductionmentioning

confidence: 91%

A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform

Anikonov,

Kazantsev,

Konovalova

2023

Journal of Inverse and Ill-Posed Problems

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Inversion Problem for Radon Transforms Defined on Pseudoconvex Sets

Anikonov,

Konovalova

2024

Dokl. Math.

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Inversion problem for Radon transforms defined on pseudoconvex sets

Anikonov,

Konovalova

2024

Doklady Rossijskoj akademii nauk. Matematika, informatika, proc

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This paper is devoted to some questions of inversion for the classical and generalized integral Radon transform. The main question is to determine information about the integrand functions if the values of some integrals are known. A feature of the work of the authors of this message is an analysis of the case when the function is integrated according to hyperplanes in finite-dimensional Euclidean space, and the integrands depend not only on the variables of integration, but also on some of the variables characterizing the hyperplanes. At the same time, the number of independent variables describing known integrals are smaller than those of the unknown integrand. We consider discontinuous integrands defined specifically introduced pseudo-convex sets. A Stefan-type problem is posed about finding surfaces discontinuities of the integrand function. The work provides formulas based on the application special integro-differential operators to known data and allowing you to solve the assigned tasks.

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A problem of integral geometry for a family of curves with incomplete data

Cited by 3 publications

References 5 publications

A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform

A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform

Inversion Problem for Radon Transforms Defined on Pseudoconvex Sets

Inversion problem for Radon transforms defined on pseudoconvex sets

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