Professor Xiang Fang

Contact

• Email: xfang@nycu.edu.tw
• Tel: ext. 56449
• Fax: +886-3-5724679
• Address: Department of Applied Mathematics, National Yang Ming Chiao Tung University,1001 Ta Hsueh Road, Hsinchu, Taiwan 30050, ROC

Teaching

• Fall Semester, 2024：
  • Real Analysis (I)
• Spring Semester, 2025：

Vitae

• Education
• Research Areas
• Positions, Honors and Awards

Selected Publications

(A)   Refereed Papers：

1. Hilbert polynomials and Arveson's curvature invariant, Journal of Functional Analysis, 198(2003), no. 2, 445-464.
2. Samuel multiplicity and the structure of Fredholm operators, Advances in Mathematics, 186(2004), no. 2, 411{437.
3. Invariant subspaces of the Dirichlet space and commutative algebra, J. Reine Angew Math., 569(2004), 189{211.
4. The Fredholm index of quotient Hilbert modules, Mathematical Research Letters, 12(2005) 911-920.
5. The Fredholm index of a pair of commuting operators, Geom. Funct. Anal. (GAFA), Vol.16.2 (2006), 367-402.
6. Canonical operator models over Reinhardt domains, Taiwanese Journal of Mathematics, Vol. 11.1, (2007) 75-94.
7. Additive Invariants on the Hardy space over the bidisk, Journal of Functional Analysis, Vol. 253 (2007) 359-372.
8. Estimates of Koszul homogoloy groups, Journal of Functional Analysis, , Vol. 255 (2008) 1-12.
9. The Fredholm index of a pair of commuting operators, II, Journal of Functional Analysis, Vol. 256 (2009) 1669-1692.
10. (With G. Cheng) An additive formula for Samuel multiplicities on Hilbert spaces of analytic functions, Journal of Functional Analysis, Vol. 260 (2011) 2027-2042.
11. (With G. Cheng) A generalization of the cellular indecomposable property via ber dimension, Journal of Functional Analysis, Vol. 260 (2011) 2964-2985.
12. (With G. Cheng) On the cellular indecomposable property of semi-Fredholm operators, Chin. Ann. Math. Ser. B Vol. 33 (2012) 903-908.
13. (With L. Chen and G. Cheng) Fiber dimension for invariant subspaces, Journal of Functional Analysis Vol. 268 (2015) 2621-2646.
14. (With Z. Wang) Two weight inequalities for the Bergman projection with doubling measures, Taiwanese Journal of Mathematics, Vol. 19 (2015) 919-926.
15. (With G. Cheng, Z. Wang and J. Yu) The hyper-singular cousin of the Bergman projection, Trans. Amer. Math. Soc. Vol. 369 (2017), no. 12, 8643-8662.
16. (With G. Cheng and S. Zhu) Random weighted shifts, Journal of Functional Analysis, Vol. 277 (2019), no. 2, 452{521.
17. (With T. Pham) A sucient condition for random zero sets of Fock spaces Archiv der Mathematik, Vol. 117 (2021), 291{304.
18. (With G. Cheng and C. Liu) A Littlewood-type theorem for random Bergman functions, Int. Math. Res. Not., Vol. 2022, Issue 14 (2022), 11056-11091.
19. (With G. Cheng, K. Guo and C. Liu) A Gaussian version of Littlewood's theorem on random power series Proc. Amer. Math. Soc., Vol. 150, number 8 (2022) 3525-3536.
20. (With T. Pham) Two problems on random entire functions in Fock spaces Canadian Journal of Mathematics Vol. 75 no. 4 (2023) 1176{1198.
https://doi.org/10.4153/S0008414X22000372
21. (With K. Guo and Z. Wang) Composition operators on the Bergman space with quasiconformal symbols Journal of Geometric Analysis. 38 pages. Vol. 33 (4). Article number: 125
(2023)
22. (With F. Guo, S. Hou, X. Zhu) Fractional integration on mixed norm spaces. II. Journal of Geometric Analysis. 37 pages. Vol. 33(5). Article number 158 (2023)
23. (With B. Chen, G. Cheng, C. Liu, T. Yu) Cesaro exponents of mixed norm spaces. Proc. Amer. Math. Soc. Vol. 151(9) (2023) 3935-3948.
24. (With B. Chen, G. Cheng, C. Liu, T. Yu) Sharp Cesaro Convergence in the Hardy Spaces Revisited. Journal of Geometric Analysis. 26 pages. Vol.33(6). Article number 290
(2023)

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