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Commutants of Toeplitz operators on the ball and annulus

  • Željko Čučković (a1) and Dashan Fan (a2)

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In this paper we study commutants of Toeplitz operators with polynomial symbols acting on Bergman spaces of various domains. For a positive integer n, let V denote the Lebesgue volume measure on ℂn. If ω is a domain in ℂn, then the Bergman space is defined to be the set of all analytic functions from ω into ℂ such that

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References

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1.Baker, I. N., Deddens, J. A. and Ullman, J. L., A theorem on entire functions with applications to Toeplitz operators, Duke Math. J. 41 (1974), 739745.
2.Cowen, C. C., The commutant dof an analytic Toeplitz operator, Trans. Amer. Math. Soc. 239 (1978) 131.
3.Čučković, Č., Commutants of Toeplitz operators on the Bergman space, Pacific J. Math. 162 (1994), 277285.
4.Deddens, J. A. and Wong, T. K., The commutant of analytic Toeplitz operators, Trans. Amer. Math. Soc. 184 (1973), 261273.
5.Shields, A. L. and Wallen, L. J., The commutants of certain Hilbert space operators, Indiana Univ. Math. J. 20 (19701971), 777788.
6.Thomson, J. E., The commutants of a class of analytic Toeplitz operators, Amer. J. Math. 99 (1977), 522529.
7.Wallsten, R., Hankel operators between weighted Bergman spaces on the ball, Ark. Mat. 28 (1990), 183192.

Commutants of Toeplitz operators on the ball and annulus

  • Željko Čučković (a1) and Dashan Fan (a2)

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