R2中混合射线变换的反演公式、独特的延拓性质和范围表征

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-05-05 DOI:10.1016/j.jmaa.2025.129637

Rohit Kumar Mishra , Suman Kumar Sahoo , Chandni Thakkar

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引用次数: 0

摘要

在本文中，我们研究了（k+ r）张量场的混合射线变换的各个方面，这些场的前k和后r指标是对称的。作为第一个结果，我们推导了一种利用混合射线变换法算子恢复未知张量场螺线形部分的反演算法。其次，我们建立了一组唯一的延拓结果。除此之外，我们还讨论了混合射线变换的范围表征作为最终结果。

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Inversion formula, unique continuation property, and range characterization of the mixed ray transform in R2

In this article, we study various aspects of the mixed ray transform of

(k + ℓ)

-tensor fields that are symmetric in its first k and last ℓ indices. As a first result, we derive an inversion algorithm to recover the solenoidal part of the unknown tensor field using the normal operator of the mixed ray transform. Next, we establish a set of unique continuation results. In addition to these, we discuss the range characterization of the mixed ray transform as the final result.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.