The paper mostly deals with the questions of closedness and essential selfadjointness of Toeplitz operators in the Segal-Bargmann space. General criteria for their closedness are formulated. Examples of unclosed Toeplitz operators are given. Explicit formulas for their adjoints are shown for various
✦ LIBER ✦
Bounded Berezin-Toeplitz Operators on the Segal-Bargmann Space
✍ Scribed by Hiroyuki Chihara
- Publisher
- SP Birkhäuser Verlag Basel
- Year
- 2009
- Tongue
- English
- Weight
- 279 KB
- Volume
- 63
- Category
- Article
- ISSN
- 0378-620X
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We study the Segal Bargmann transform on a symmetric space X of compact type, mapping L 2 (X ) into holomorphic functions on the complexification X C . We invert this transform by integrating against a ``dual'' heat kernel measure in the fibers of a natural fibration of X C over X. We prove that the