Academic Areas: Analysis
Research Interests: Harmonic and Functional Analysis
Academic Degrees
PhD, 1997, Department of Mathematics, University of Tubingen, Germany;
Master, 1988, Department of Mathematics, Sichuan University, China;
Bachelor, 1984, Department of Mathematics, Sichuan University, China.
Professional Experience
Professor (1993-present); School of Mathematics and statistics, Huazhong University of Science and Technology;
Professor (2003-2006); School of Mathematics and statistics, Huazhong Normal University;
Professor (1998-2006); School of Mathematics and statistics, Lanzhou University;
Associate Professor (1991-1993); Department of Mathematics, Huazhong University of Science and Technology;
Assistant (1988-1991); Department of Mathematics, Huazhong University of Science and Technology;
Assistant (1984-1985); Department of Mathematics, Sichuan University, China.
Selected Publications
1. (with M. Li) Regularized Semigroups and Non-Elliptic Differential Operators, Science Press, Beijing, 2014.
2. Strongly Continuous Semigroups of Linear Operators (in Chinese), Huazhong Univ. of Sci. and Tech. Press, 1994.
3. (with S. Huang, X. Yao) Remarks on Lp-limiting absorption principle of Schrödinger operators and applications to spectral multiplier theorems, Froum Math. (to appear).
4. (with T. Huang, S. Huang) Inhomogeneous oscillatory integrals and global smoothing effects for dispersive equations, J. Differential Equations, 263(2017), 8606-8629.
5. (with Z. Duan, J. Feng) Long range scattering for higher order Schrödinger operators, J. Differential Equations, 254(2013), 3329-3351.
6. (with X. Yao) Higher order Kato class potentials for Schrödinger operators, Bull. London Math. Soc. 41(2009), 293-301.
7. (with M. Li) Extrapolation spaces for C-semigroups, Proc. Amer. Math. Soc., 137(2009), 663-668.
8. (with J. Qiang, M. Li) The applications of C-semigroups to the Dirac equation, Appl. Math. Lett., 22(2009), 422-427.
9. (with X. Yao) Oscillatory integrals and Lp estimates for Schrödinger equations, J. Differential Equations, 244(2008), 741-752.
10. (with L. Li, X. Yao, D. Fan) The spectrum of differential operators in Hp spaces, Illinois J. Math., 49(2005), 45-62.
11. (with Y. Huang) Regularization for a class of ill-posed Cauchy problems, Proc. Amer. Math. Soc., 133(2005), 3005-3012.
12. (with X. Yao, D. Fan) Convex hypersurfaces and Lp estimates for Schrödinger equations, J. Funct. Anal., 208(2004), 122-139.
13. (with Y. Huang) Regularization for ill-posed Cauchy problems associated with generators of analytic semigroups, J. Differential Equations, 203(2004), 38-54.
14. (with I. Mel’nikova, J. Zhang) Regularization of weakly ill-posed Cauchy problems, J. Inverse and Ill-Posed Problems, 10(2002), 385-393.
15. Applications of semigroups of operators to non-elliptic differential operators, Chinese Sci. Bull., 45(2000), 673-682.
16. (with J. Zhang) Gaussian estimates and regularized groups, Proc. Amer. Math. Soc., 127(1999), 1089-1096.
17. (with Y. Li) Abstract parabolic systems and regularized semigroups, Pacific J. Math., 182(1998), 183-199.
18. (with L. Liu) Almost periodic regularized groups, semigroups, and cosine functions, J. Math. Anal. Appl., 197(1996), 90-112.
19. Controllability of a class of linear systems in Banach space, Proc. Amer. Math. Soc., 123(1995), 1241-1251.
20. (with Y. Lei, W. Yi) Semigroups of operators and polynomials of generators of bounded strongly continuous groups, Proc. London Math. Soc., 69(1994), 144-170.
21. Strongly continuous M,N-families of bounded operators, Integral Equations Operator Theory, 19(1994), 105-119.
22. A Hille-Yosida theorem for the higher order abstract Cauchy problem, Bull. London Math. Soc., 24(1992), 531-539.
23. Solvability and well-posedness of higher-order abstract Cauchy problems, Sci. China (Series A), 34(1991), 147-156.
24. (with Z. Liu) Fixed point theorems for fuzzy mappings, in “Uncertainty and Intelligent Systems” (B. Bouchon, L. Saitta, and R. R. Yager eds.), Lecture Notes in Computer Science, Springer-Verlag, 313(1988), 33-40.
Awards:
1993: “Outstanding Expert” awarded by Hubei Provincial Government
1993: “Government Special Allowance” awarded by the State Council, PRC
1995: “The Prize of Monograph” awarded by MOE (Ministry of Education, PRC)
1997: “The Third Prize for Science and Technology Advancement” awarded by MOE
1997: “The Prize for outstanding young teachers” awarded by Fok Ying Tung education foundation
2000: “The Second Prize for Science Advancement” awarded by Hubei Provincial Government
2002: “The Prize for outstanding young teachers in higher education institutions” awarded by MOE
2003: “The Third Prize for Science and Technology Advancement” awarded by Hubei Provincial Government
Courses Taught
Taught more than 20 courses, such as Real Analysis, Functional analysis, Harmonic analysis, Oscillatory integrals, Analysis of linear Partial Differential operators, Methods of modern mathematical physics, Schrodinger operators
Project
Completed more than 10 foundations from National Natural Science Foundation and Ministry of Education of China
Chinese