Commuting Toeplitz operators on the Segal–Bargmann space
| Autor: | Young Joo Lee, Wolfram Bauer |
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| Rok vydání: | 2011 |
| Předmět: |
Mathematics::Functional Analysis
Pure mathematics 010102 general mathematics Commutator (electric) Operator theory Space (mathematics) 01 natural sciences Toeplitz matrix law.invention 010101 applied mathematics Algebra Radial function Toeplitz operator law Reproducing kernel Hilbert space Bounded function Radial symbol 0101 mathematics Complex plane Mellin transform Analysis Mathematics Counterexample |
| Zdroj: | Journal of Functional Analysis. 260:460-489 |
| ISSN: | 0022-1236 |
| DOI: | 10.1016/j.jfa.2010.09.007 |
| Popis: | Consider two Toeplitz operators T g , T f 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 [ T g , T f ] = 0 does not imply the radial dependence of f. Finally, we consider Toeplitz operators on the Segal–Bargmann space over C n and n > 1 , where the commuting property of Toeplitz operators can be realized more easily. |
| Databáze: | OpenAIRE |
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