Эта публикация цитируется в 1 статье

Вещественный, комплексный и и функциональный анализ

The ray transform of symmetric tensor fields with incomplete projection data on a convex non-smooth domain

N. A. Vaytsel

Novosibirsk State University, 2, Pirogova str., 630090, Novosibirsk, Russia

Аннотация: We consider the ray transform $I_\Gamma$ that integrates symmetric rank $m$ tensor fields on $\mathbb{R}^n$ supported in a bounded convex domain $D \subset \mathbb{R}^n$ over lines. The integrals are known for the family $\Gamma$ of lines $l$ such that endpoints of the segment $l \cap D$ belong to a given part $\gamma = \partial D \cap \mathbb{R}^n_{+}$ of the boundary, for some half-space $R^n_{+}\subset \mathbb{R}^n$. In this work, we assume that the domain $D$ is convex with a non-smooth boundary. In this case, we prove that the kernel of the operator $I_\Gamma$ coincides with the space of $\gamma$-potential tensor fields, which is a generalization of the results obtained in [2].

Ключевые слова: tomography with incomplete data, ray transform, tensor analysis.

УДК: 517.9

MSC: 44A12, 46F12

Поступила 7 марта 2023 г., опубликована 8 ноября 2024 г.

Язык публикации: английский

DOI: 10.33048/semi.2024.21.067