Details
| Original language | English |
|---|---|
| Pages (from-to) | 2989-2996 |
| Number of pages | 8 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 132 |
| Issue number | 10 |
| Publication status | Published - 2 Jun 2004 |
| Externally published | Yes |
Abstract
This paper considers Hankel operators on the Segal-Bargmann space of holomorphic functions on ℂn that are square integrable with respect to the Gaussian measure. It is shown that in the case of a bounded symbol g ε L∞ (ℂn) the Hankel operator Hg is of the Hilbert-Schmidt class if and only if Hḡ is Hilbert-Schmidt. In the case where the symbol is square integrable with respect to the Lebesgue measure it is known that the Hilbert-Schmidt norms of the Hankel operators Hg and Hḡ coincide. But, in general, if we deal with bounded symbols, only the inequality ∥H g∥HS ≤ 2∥Hḡ∥HS can be proved. The results have a close connection with the well-known fact that for bounded symbols the compactness of Hg implies the compactness of Hḡ.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Proceedings of the American Mathematical Society, Vol. 132, No. 10, 02.06.2004, p. 2989-2996.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Hilbert-Schmidt Hankel Operators On The Segal-Bargmann Space
AU - Bauer, Wolfram
N1 - Copyright: Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2004/6/2
Y1 - 2004/6/2
N2 - This paper considers Hankel operators on the Segal-Bargmann space of holomorphic functions on ℂn that are square integrable with respect to the Gaussian measure. It is shown that in the case of a bounded symbol g ε L∞ (ℂn) the Hankel operator Hg is of the Hilbert-Schmidt class if and only if Hḡ is Hilbert-Schmidt. In the case where the symbol is square integrable with respect to the Lebesgue measure it is known that the Hilbert-Schmidt norms of the Hankel operators Hg and Hḡ coincide. But, in general, if we deal with bounded symbols, only the inequality ∥H g∥HS ≤ 2∥Hḡ∥HS can be proved. The results have a close connection with the well-known fact that for bounded symbols the compactness of Hg implies the compactness of Hḡ.
AB - This paper considers Hankel operators on the Segal-Bargmann space of holomorphic functions on ℂn that are square integrable with respect to the Gaussian measure. It is shown that in the case of a bounded symbol g ε L∞ (ℂn) the Hankel operator Hg is of the Hilbert-Schmidt class if and only if Hḡ is Hilbert-Schmidt. In the case where the symbol is square integrable with respect to the Lebesgue measure it is known that the Hilbert-Schmidt norms of the Hankel operators Hg and Hḡ coincide. But, in general, if we deal with bounded symbols, only the inequality ∥H g∥HS ≤ 2∥Hḡ∥HS can be proved. The results have a close connection with the well-known fact that for bounded symbols the compactness of Hg implies the compactness of Hḡ.
UR - http://www.scopus.com/inward/record.url?scp=5644266304&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-04-07264-8
DO - 10.1090/S0002-9939-04-07264-8
M3 - Article
AN - SCOPUS:5644266304
VL - 132
SP - 2989
EP - 2996
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 10
ER -