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Lvchang Li

Publications and source records attributed to Lvchang Li.

5 recordsLinked to original sources
arXiv2026

Characterization of Attenuated V-Line Transform and Direct Reconstruction from Samples

The V-line transform (V-LT), a generalized Radon transform (RT), is widely used in Compton scattering imaging (CSI). The central mathematical problem of CSI is to reconstruct a function from its V-LT. Unlike V-LT, the attenuated V-line transform (AV-LT) accounts for the medium-induced loss of intensity, and has been demonstrated to improve image quality. The present paper makes two main contributions. (1) We establish the fundamental characterizations for AV-LT including operator properties ($L^2$-boundedness, operator norm etc.), a necessary and sufficient condition for the preservation of compact support, and sharp estimation of Sobolev smoothness. These characterizations remain unexplored, and they reveal essential differences among AV-LT, RT and V-LT. (2) We develop a direct reconstruction method based on AV-LT samples that does not require solving any equation. Our sampling formula gives exact reconstruction for band-limited functions. We also provide approximate reconstruction for functions in $H^s(\mathbb{R}^2)$ with $s>2$.

math.FA↗
arXiv2024

Difference of composition operators on Korenblum spaces over tube domain

The Korenblum space, often referred to as a growth space, is a special type of analytic function space. This paper investigates the properties of the difference of composition operators on the Korenblum space over the product of upper half planes, characterizing their boundedness and compactness. Using the result on boundedness, we show that all bounded differences of composition operators are absolutely summable operators.

math.FA↗
arXiv2024

Boundedness of Multiparameter Forelli-Rudin Type Operators on Product $L^p$ Spaces over Tubular Domains

In this paper, we introduce and study two classes of multiparameter Forelli-Rudin type operators from $L^{\vec{p}}\left(T_B\times T_B, dV_{α_1}\times dV_{α_2}\right)$ to $L^{\vec{q}}\left(T_B\times T_B, dV_{β_1}\times dV_{β_2}\right)$, especially on their boundedness, where $L^{\vec{p}}\left(T_B\times T_B, dV_{α_1}\times dV_{α_2}\right)$ and $L^{\vec{q}}\left(T_B\times T_B, dV_{β_1}\times dV_{β_2}\right)$ are both weighted Lebesgue spaces over the Cartesian product of two tubular domains $T_B\times T_B$, with mixed-norm and appropriate weights. We completely characterize the boundedness of these two operators when $1\le \vec{p}\le \vec{q}<\infty$. Moreover, we provide the necessary and sufficient condition of the case that $\vec{q}=(\infty,\infty)$. As an application, we obtain the boundedness of three common classes of integral operators, including the weighted multiparameter Bergman-type projection and the weighted multiparameter Berezin-type transform.

math.FA↗
arXiv2024

Toeplitz Operators on Weighted Bergman Spaces over Tubular Domains

In this paper, we mainly study the necessary and sufficient conditions for the boundedness and compactness of Toeplitz operators on weighted Bergman spaces over a tubular domains by using the Carlson measures on tubular domains. We also give some related results about Carlson measures.

math.CV↗