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    Article

    Complex symmetric Toeplitz operators on the Hardy spaces and Bergman spaces

    In this paper, we first completely characterize the complex symmetric Toeplitz operators \(T_\varphi \) ...

    **aohe Hu, Cui Wang, Zhiyuan Xu in Annals of Functional Analysis (2024)

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    Article

    Disjoint hypercyclic and supercyclic composition operators on discrete weighted Banach spaces

    In this paper, we characterize the disjoint hypercyclic and disjoint supercyclic composition operators on the little weighted Banach space $$L^0_\mu (...

    Zhiyuan Xu, Ya Wang, Zehua Zhou in Collectanea Mathematica (2023)

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    Article

    Hypercyclic exponential of the differential operator on Banach spaces related to Fock spaces

    In this note, we give the mixing, and therefore hypercyclic, property of the exponential of the differential operator on Banach spaces related to Fock spaces. Besides, we also characterize the mixing property ...

    Zhiyuan Xu, Zehua Zhou in Annals of Functional Analysis (2023)

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    Article

    Complex symmetry of linear combinations of composition operators on the Fock space

    In this paper, we solve a new problem about complex symmetry. We give a complete characterization of linear combinations of composition operators on the Fock space and the normality and self-adjointness for co...

    Zhiyuan Xu, Zicong Yang, Zehua Zhou in Archiv der Mathematik (2022)

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    Article

    On the generalized Chern conjecture for hypersurfaces with constant mean curvature in a sphere

    Let M be a compact hypersurface with constant mean curvature in \({\mathbb{S}^{n + 1}}\) . Denote by H and S the mean curvature ...

    Li Lei, Hongwei Xu, Zhiyuan Xu in Science China Mathematics (2021)

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    Article

    A generalization of Pólya conjecture and Li–Yau inequalities for higher eigenvalues

    We verify that if M is a compact minimal submanifold with boundary in a Cartan–Hadamard manifold N, then $$\sum \nolimits _{i=1}^{k}\lambda _i\ge \frac{2n\pi }{e}k^{\frac{n+2}{n}}{{\,\mathrm{vol}\,}}(M)^{-\frac{...

    Zhiyuan Xu, Hongwei Xu in Calculus of Variations and Partial Differential Equations (2020)

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    Article

    A new pinching theorem for complete self-shrinkers and its generalization

    In this paper, we firstly verify that if Mn is an n-dimensional complete self-shrinker with polynomial volume growth in ℝn+1, and if the squared norm of the second fundamental form of M satisfies $$0\leqslant S ...

    Li Lei, Hongwei Xu, Zhiyuan Xu in Science China Mathematics (2020)