（1）函数空间上的算子理论和算子代数。

（2）Hilbert空间上的控制理论。

发表论文：

1.  Li, Yufei, Yang, Yixin, Lu, Yufeng Reducibility and unitary equivalence for a class of truncated Toeplitz operators on model spaces. New York J. Math. 24 (2018), 929–946. 47B35 (47A15)

2.  Cui, Puyu,  Lu, Yufeng,  Shi, Yanyue Hyponormality of Toeplitz operators with polynomial symbols on the vector valued Bergman space. Oper. Matrices12 (2018), no. 3, 787–796.

3.  Hu, Yinyin; Deng, Jia; Yu, Tao; Liu, Liu; Lu, Yufeng Reducing subspaces of the dual truncated Toeplitz operator. J. Funct. Spaces 2018, Art. ID 7058401, 9 pp. 47B33

4.  Kong, Linghui; Lu, Yufeng Some algebraic properties of dual Toeplitz operators. Houston J. Math. 44 (2018), no. 1, 169–185. 47B35 (47B38)

5. Deng, Jia; Lu, Yufeng; Shi, Yanyue; Hu, Yinyin Reducing subspaces for a class of nonanalytic Toeplitz operators. Banach J. Math. Anal. 12 (2018), no. 2,456–480.

6.  Kong, Linghui; Lu, Yufeng Toeplitz operators on weighted pluriharmonic Bergman space. Banach J. Math. Anal. 12 (2018), no. 2, 439–455.

7.  Li, Yufei; Lu, Yufeng; Yu, Tao The essential norms of composition operators on weighted Dirichlet spaces. Bull. Aust. Math. Soc. 97 (2018), no. 2, 297–307. 

8. Yang, Zhitao; Zhang, Bo; Lu, Yufeng Dual Toeplitz operators on the unit ball. J. Math. Res. Appl. 37 (2017), no. 6, 710–724.

9.  Ding, Qian; Hu, Yinyin; Liu, Liu; Lu, Yufeng Zero products and finite rank of Toeplitz operators on the harmonic Bergman space. J. Math. Res. Appl. 37(2017), no. 3, 325–334. 47B35 (30H20 31A05)

10.  Liu, Liu; Lu, Yufeng Analysis on the time-varying gap of discrete time-varying linear systems. Oper. Matrices 11 (2017), no. 2, 533–555.

11. Azari Key, Fatemeh; Lu, Yufeng; Yang, Rongwei On numerical invariants for homogeneous submodules in H2(D2). New York J. Math. 23 (2017), 505–526.

12.  Ding, Qian; Chen, Yong; Lu, Yufeng Commuting Toeplitz and Hankel operators on harmonic Dirichlet spaces. J. Funct. Spaces 2017, Art. ID 9627109, 8 pp.

13. Yang, Zhi Tao; Lu, Yu Feng; Cheng, Qing Jin Super weak compactness and uniform Eberlein compacta. Acta Math. Sin. (Engl. Ser.) 33 (2017), no. 4, 545–553.

14. Deng, Jia; Lu, Yufeng; Shi, Yanyue Reducing subspaces for a class of non-analytic Toeplitz operators on the bidisk. J. Math. Anal. Appl. 445 (2017), no. 1,784–796.

15. Lin, Hong Zhao; Hu, Yin Yin; Lu, Yu Feng Reducing subspaces of Toeplitz operators on the weighted Dirichlet space of the bidisk. (Chinese) Chinese Ann. Math. Ser. A 37 (2016), no. 3, 311–328. 47B35

16.  Lu, Yufeng; Azari Key, Fatemeh; Yang, Hewei; Liu, Liu Algebraic properties of dual Toeplitz operators on harmonic Hardy space over polydisc. J. Math. Res. Appl. 36 (2016), no. 6, 703–710.

17.  Yang, Jingyu; Lu, Yufeng; Wang, Xiaoying Algebraic properties of Toeplitz operators on the harmonic Bergman space. J. Math. Res. Appl. 36 (2016), no. 4,495–504.

 18. Song, Shuyan; Liu, Liu; Lu, Yufeng On the simultaneous stabilization of linear time-varying systems. J. Math. Res. Appl. 36 (2016), no. 3, 341–350.

19.  Li, Ran; Lu, Yufeng (m,λ)-Berezin transform on the weighted Bergman spaces over the polydisk. J. Funct. Spaces 2016, Art. ID 6804235, 11 pp. 47B33

20.  Yang, Jing Yu; Hu, Yin Yin; Lu, Yu Feng; Yu, Tao Commuting dual Toeplitz operators on the harmonic Dirichlet space. Acta Math. Sin. (Engl. Ser.) 32(2016), no. 9, 1099–1105.