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01151nam a2200181Ia 4500 |
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10.1090-tran-8638 |
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220425s2022 CNT 000 0 und d |
| 020 |
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|a 00029947 (ISSN)
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| 245 |
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|a SCHATTEN CLASS HANKEL OPERATORS ON THE SEGAL-BARGMANN SPACE AND THE BERGER-COBURN PHENOMENON
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| 260 |
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|b American Mathematical Society
|c 2022
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| 856 |
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|z View Fulltext in Publisher
|u https://doi.org/10.1090/tran/8638
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|a We give a complete characterization of Schatten class Hankel operators Hf acting on weighted Segal-Bargmann spaces F2(φ) using the notion of integral distance to analytic functions in Cn and Hörmander's ∂-theory. Using our characterization, for f ∈ L∞ and 1 < p < ∞, we prove that Hf is in the Schatten class Sp if and only if H f ∈ Sp, which was previously known only for the Hilbert-Schmidt class S2 of the standard Segal-Bargmann space F2(φ) with φ(z) = α|z|2. © 2022 American Mathematical Society.
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|a Hankel operator
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|a Schatten class
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|a Segal-Bargmann space
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|a Hu, Z.
|e author
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|a VIRTANEN, J.A.
|e author
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| 773 |
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|t Transactions of the American Mathematical Society
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