论文标题
Segal-Bargmann空间上的Toeplitz运营商的自我相关性
Self-Adjointness of Toeplitz Operators on the Segal-Bargmann Space
论文作者
论文摘要
我们证明了一个新的标准，可以保证具有无限型操作员值符号的Toeplitz运营商的自我偶像性。我们的标准尤其适用于Lipschitz连续衍生物的符号，这是古典力学的自然级别函数。为此，我们将Berger-Coburn估计值扩展到矢量值Segal-Bargmann空间。最后，我们将结果应用于Schrödinger代表中的Schwartz函数空间上的一类（操作员值）二次形式的自我相关性。
We prove a new criterion that guarantees self-adjointness of Toeplitz operator with unbounded operator-valued symbols. Our criterion applies, in particular, to symbols with Lipschitz continuous derivatives, which is the natural class of Hamiltonian functions for classical mechanics. For this we extend the Berger-Coburn estimate to the case of vector-valued Segal-Bargmann spaces. Finally, we apply our result to prove self-adjointness for a class of (operator-valued) quadratic forms on the space of Schwartz functions in the Schrödinger representation.
