标题： H-Toeplitz 算子在 Fock 空间上 显示英文标题

标题： H-Toeplitz operators on Fock space

摘要： 本文探讨了Fock空间上的H-Toeplitz算子，统一了Toeplitz和Hankel算子的某些方面，并引入了新的结构特性。 我们推导了这些算子在单变量正交基下的显式矩阵表示，分析了它们的对易性，并建立了紧性准则。 关键结果包括对具有调和符号的对易H-Toeplitz算子的表征，以及证明非零的H-Toeplitz算子不能是Hilbert-Schmidt算子。 此外，我们引入了定向H-Toeplitz图来可视化由这些算子编码的相邻关系，通过入度和出度序列展示了它们的结构模式。 我们的研究将理论算子理论与图形表示联系起来，为解析函数空间与算子代数之间的相互作用提供了见解。 显示英文摘要

摘要： This paper explores H-Toeplitz operators on the Fock space, unifying aspects of Toeplitz and Hankel operators while introducing novel structural properties. We derive explicit matrix representations for these operators with respect to the orthonormal basis of monomials, analyze their commutativity, and establish compactness criteria. Key results include the characterization of commuting H-Toeplitz operators with harmonic symbols and the proof that non-zero H-Toeplitz operators cannot be Hilbert-Schmidt. Additionally, we introduce directed H-Toeplitz graphs to visualize adjacency relations encoded by these operators, demonstrating their structural patterns through indegree and outdegree sequences. Our findings bridge theoretical operator theory with graphical representations, offering insights into the interplay between analytic function spaces and operator algebras.