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圆环上的Dirichlet空间及其算子 被引量:3

Dirichlet Space on Annulus and Its Operators
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摘要 本文主要讨论了圆环上Dirichlet空间中Toeplitz算子的Fredholm性质,计算了符号在C^1和H_1~∞+C^1中的Toeplitz算子的本性谱. In this paper, the Predholm properties of some Toeplitz operators on Dirichlet spaces are discussed, and the essential spectra of Toeplitz operators with symbols in C1 or H1∞?+ C1 are computed.
出处 《数学学报(中文版)》 SCIE CSCD 北大核心 2003年第4期761-770,共10页 Acta Mathematica Sinica:Chinese Series
基金 国家自然科学基金(19971061)
关键词 圆环 TOEPLITZ算子 本性谱 Fredholm指标 Annulus Toeplitz operator Essential spectra Fredholm index
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参考文献4

  • 1Alxer S., Conway J. B., McDonald G., Toeplitz operators on Bergman spaces, Can. J. Math., 1982, 84(2):466-483.
  • 2Cao G. F., Fredholm properties of Toeplitz operators on Dirichlet spaces, Pacific Journal of Mathmatics, 1999,188: 209-223.
  • 3Cao G. F., Waug X. F., Operators on Bergman spaces for Riemann surfaces, preprint.
  • 4Douglas R. G., Banach algebra techniques in operator, New York, London: Academics Press, 1972.

同被引文献24

  • 1ZHU K H. Hankel-Toeplitz operators on La^1 (Ω)[J]. Integ Equ Ope Theor, 1990,13: 285-302.
  • 2王汝发.圆环上的Bergman空间中Toeplitz算子[D].兰州:甘肃政法学院,1998.
  • 3李德生,罗生英.圆环上的Bergman空间、Bergman度量及圆环的分解理论[D].吉昌:河池师专,1995.
  • 4JARI T, JANNI A V. Spectral of Toeplitz and Hankel operators on the Bergman space A^I [J]. New York J Math, 2008,14: 305-323.
  • 5XIANG Y X. Toeplitz-Hankel type operators on La^1 (Ω) [J]. J Math Tech, 2001,17:8-11.
  • 6ZHU K H. Mutipliers of BMO in the Bergman metric with applications to Toephtz operators [ J ]. J Funct Anal, 1989,87: 31-50.
  • 7DOUGLAS R G. Banach algebra techniques in operator theory[M]. New York and London: Academic Press, 1972.
  • 8MIRJANA J, ZHENG D C. Compact operators and Toeplitz algebras on multiply-connected domains[ J]. J Funct Anal, 2011,25:25-50.
  • 9William T R. The classical Dirichlet space. J Amer Math Soc, 2006, (2006): 171- 197.
  • 10Richard R, Zhijian Wu. Toeplitz operator on Diriehlet spaces. J Inter Equat Oper Th, 1992, 115:325 -342.

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