Commuting Toeplitz operators on the Segal-Bargmann space |
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Authors: | Wolfram Bauer Young Joo Lee |
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Affiliation: | a Mathematisches Institut, Georg-August-Universität, Bunsen-str. 3-5, 37073 Göttingen, Germany b Department of Mathematics, Chonnam National University, Gwangju 500-757, Republic of Korea |
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Abstract: | Consider two Toeplitz operators Tg, Tf on the Segal-Bargmann space over the complex plane. Let us assume that g is a radial function and both operators commute. Under certain growth condition at infinity of f and g we show that f must be radial, as well. We give a counterexample of this fact in case of bounded Toeplitz operators but a fast growing radial symbol g. In this case the vanishing commutator [Tg,Tf]=0 does not imply the radial dependence of f. Finally, we consider Toeplitz operators on the Segal-Bargmann space over Cn and n>1, where the commuting property of Toeplitz operators can be realized more easily. |
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Keywords: | Toeplitz operator Mellin transform Reproducing kernel Hilbert space Radial symbol |
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