向量值Bergman空间上块Toeplitz算子的零积问题
Zero Product Problem of Block Toeplitz Operator in Vector Value Bergman Space
摘要: 本文给出了向量值Bergman空间上块Toeplitz算子TFTG = 0的一个充分必要条件,其中F为一般本性有界向量值函数,G为调和多项式。
Abstract: We give a necessary and sufficient condition for the block Toeplitz operator on vector value Bergman space, where F is the bounded vector value function of general nature, G is harmonic polynomial.
文章引用:张楠, 关印, 尚巍. 向量值Bergman空间上块Toeplitz算子的零积问题[J]. 应用数学进展, 2018, 7(12): 1521-1529. https://doi.org/10.12677/AAM.2018.712177

参考文献

[1] Basor, E.L. and Ehrhardt, T. (2007) Asymptotics of Block Toeplitz Determinants and the Classical Dimer Model. Communications in Mathematical Physics, 274, 427-455. [Google Scholar] [CrossRef
[2] Hikami, K. and Imamura, T. (2003) Vicious Walkers and Hook Young Tableaux. Journal of Physics A: Mathematical and General, 36, 3033-3048. [Google Scholar] [CrossRef
[3] Cafasso, M. (2008) Block Toeplitz Determinants, Constrained KP and Gelfand-Dickey Hierarchies. Mathematical Physics Analysis and Geometry, 11, 11-51. [Google Scholar] [CrossRef
[4] Brown, A. and Halmos, P.R. (1964) Algebraic Properties of Toeplitz Operators. Journal für die reine und Angewandte Mathematik, 213, 89-102.
[5] Guo, K. (1996) A Problem on Products of Toeplitz Operators. Proceedings of the American Mathematical Society, 124, 869-871. [Google Scholar] [CrossRef
[6] Gu, C. (2000) Products of Several Toeplitz Operators. Journal of Functional Analysis, 171, 483-527. [Google Scholar] [CrossRef
[7] Aleman, A. and Vukotic, D. (2009) Zero Products of Toeplitz Oper-ators. Duke Mathematical Journal, 148, 373-403. [Google Scholar] [CrossRef
[8] Čučković, Ž. (2003) Berezin versus Mellin. Journal of Mathe-matical Analysis and Applications, 287, 234-243. [Google Scholar] [CrossRef
[9] Lu, Y.F. and Shang, S.X. (2009) Bounded Hankel Products on the Bergman Space of the Polydisk. Canadian Journal of Mathematics, 61, 190-204. [Google Scholar] [CrossRef
[10] Lu, Y.F. and Liu, C.M. (2009) Toeplitz and Hankel Products on Bergman Spaces of the Unit Ball. Chinese Annals of Mathematics (Series B), 30, 293-310. [Google Scholar] [CrossRef
[11] Yu, T. and Zhu, R.W. (2011) Toeplitz Products on Vector-Valued Bergman Spaces of the Unit Ball. Acta Mathematica Scientia, 31A, 1550-1558.
[12] Remmert, R. (1998) Classical Topics in Complex Function Theory. Graduate Texts in Methematics. Springer, New York.