people:xxu:xxu-personal
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| <LI><P><FONT SIZE=4 STYLE="font-size: 14pt"> | <LI><P><FONT SIZE=4 STYLE="font-size: 14pt"> | ||
| - | Detailed study of the spectral theory of elliptic operators (Laplace operator and Schrödinger operator) on compact or complete manifolds, in particular, on the growth estimates (Lp, bilinear, and gradient estimates) of eigenfunctions, multiplier problems, Carleson measures and Logvinenko-Sereda sets on compact or complete manifolds with or without boundary. | + | Detailed study of the spectral theory of elliptic operators (Laplace operator and Schrödinger operator) on compact or complete manifolds. Mainly focus on on the growth estimates (Lp, bilinear, and gradient estimates) of eigenfunctions and spectral clusters, and apply these estimates to multiplier problems, characterization of $L^p$-Carleson measures and $L^p$-Logvinenko-Sereda sets on compact or complete manifolds with or without boundary. |
| </FONT></FONT></P> | </FONT></FONT></P> | ||
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| <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | ||
| Huichao Chen, <B>Xiangjin Xu</B>, Power analysis of a left-truncated normal mixture distribution with | Huichao Chen, <B>Xiangjin Xu</B>, Power analysis of a left-truncated normal mixture distribution with | ||
| - | applications in red blood cell velocities. Presentation (by <B>H. Chen</B>) at Joint Statistical Meetings (JSM), | + | applications in red blood cell velocities. Presented (by <B>H. Chen</B>), Joint Statistical Meetings (JSM), |
| Montreal, August, 2013.(<A HREF="CX-poweranalysis.pdf"></A>)</FONT></P> | Montreal, August, 2013.(<A HREF="CX-poweranalysis.pdf"></A>)</FONT></P> | ||
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| <B>Xiangjin Xu</B>, Characterization of Carleson Measures via Spectral Estimates on Compact Manifolds with Boundary. Springer Proceedings in Mathematics & Statistics, vol 471. Page 1-23, Springer,2024. <A HREF="https://doi.org/10.1007/978-3-031-69706-7_1">https://doi.org/10.1007/978-3-031-69706-7_1</A>(<A HREF="Xu-Carleson.pdf"></A>)</FONT></P> | <B>Xiangjin Xu</B>, Characterization of Carleson Measures via Spectral Estimates on Compact Manifolds with Boundary. Springer Proceedings in Mathematics & Statistics, vol 471. Page 1-23, Springer,2024. <A HREF="https://doi.org/10.1007/978-3-031-69706-7_1">https://doi.org/10.1007/978-3-031-69706-7_1</A>(<A HREF="Xu-Carleson.pdf"></A>)</FONT></P> | ||
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| + | <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | ||
| + | Xing Wang,<B>Xiangjin Xu</B>, Cheng Zhang, $L^p$-Logvinenko-Sereda sets and $L^p$-Carleson measures on compact manifolds. Adv. Math. Volume 494, June 2026, 110958 <A HREF="https://doi.org/10.1016/j.aim.2026.110958"> https://doi.org/10.1016/j.aim.2026.110958 <A HREF="arXiv:2506.22759"></A>arXiv:2506.22759 [math.AP]. | ||
| + | </FONT></P> | ||
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| + | <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | ||
| + | Huichao Chen, Chengxing Lu, Xiaomei Liao, <B>Xiangjin Xu</B>, Ronald Bosch, Modeling Viral Rebound in HIV Cure Trials: An Application of the Accelerated Failure Time Framework. Presented (by <B>H. Chen</B>), Biopharmaceutical Section. Joint Statistical Meetings (JSM),Boston, MA. August 4th, 2026.(<A HREF="CX-poweranalysis.pdf"></A>)</FONT></P> | ||
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| </OL> | </OL> | ||
| </TD> | </TD> | ||
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| (<A HREF="Xu-HeatKernel-II.pdf"></A>)</FONT></P> | (<A HREF="Xu-HeatKernel-II.pdf"></A>)</FONT></P> | ||
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| - | + | <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | |
| - | <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | + | <B>Xiangjin Xu</B>, New uniqueness criteria of tangent cones for manifolds with nonnegative Ricci curvature. (preprint) (<A HREF="LX-DHI-II.pdf"></A>)</FONT></P> |
| - | Xing Wang,<B>Xiangjin Xu</B>, Cheng Zhang, $L^p$-Logvinenko-Sereda sets and $L^p$-Carleson measures on compact manifolds. arXiv:2506.22759 [math.AP]. (Submitted July 2025) | + | |
| - | (<A HREF="Xu-HeatKernel-II.pdf"></A>)</FONT></P> | + | |
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| <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | ||
| - | <B>Xiangjin Xu</B>, Differential Harnack inequalities on Riemannian manifolds II: Schr\"odinger operator. (In Progress) (<A HREF="LX-DHI-II.pdf"></A>)</FONT></P> | + | <B>Xiangjin Xu</B>, Differential Harnack inequalities on Riemannian manifolds II: Schr\"odinger operator. (preprint) (<A HREF="LX-DHI-II.pdf"></A>)</FONT></P> |
| <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | ||
| - | <B>Xiangjin Xu</B>, The Perelman-type entropy formula for linear heat equation on noncompact manifolds. (In Progress) (<A HREF="LX-DHI-II.pdf"></A>)</FONT></P> | + | <B>Xiangjin Xu</B>, The Perelman-type entropy formula for linear heat equation on noncompact manifolds. (preprint) (<A HREF="LX-DHI-II.pdf"></A>)</FONT></P> |
| - | + | ||
| - | + | ||
| - | <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | + | |
| - | <B>Xiangjin Xu</B>, New uniqueness criteria of tangent cones for manifolds with nonnegative Ricci curvature. (In Progress) (<A HREF="LX-DHI-II.pdf"></A>)</FONT></P> | + | |
| <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | ||
| - | <B>Xiangjin Xu</B>, Multiple periodic solutions of super-quadratic Hamiltonian systems with bounded forcing | + | <B>Xiangjin Xu</B>, Pricise estimates on the rates to equilibrium of the heat kernels on compact rank one symmetric spaces. (preprint) (<A HREF="Xu-HS-BF.pdf"></A>)</FONT></P> |
| - | terms.(In Progress) (<A HREF="Xu-HS-BF.pdf"></A>)</FONT></P> | + | |
| <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | ||
| - | <B>Xiangjin Xu</B>, Periodic and subharmonic solutions of Hamiltonian systems possessing "super-quadratic" potentials. (In Progress) (<A HREF="Xu-HS-SQ.pdf"></A>)</FONT></P> | + | <B>Xiangjin Xu</B>, Periodic and subharmonic solutions of Hamiltonian systems possessing "super-quadratic" potentials. (preprint) (<A HREF="Xu-HS-SQ.pdf"></A>)</FONT></P> |
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| + | <LI><P><FONT SIZE=4 STYLE="font-size: 16pt"> | ||
| + | <B>Xiangjin Xu</B>, Characterization of Carleson Measures via Spectral Estimates for Dirichlet Laplacian. (preprint) (<A HREF="Xu-HS-SQ.pdf"></A>)</FONT></P> | ||
| </OL> | </OL> | ||
people/xxu/xxu-personal.1769701546.txt · Last modified: 2026/01/29 10:45 by xxu