广义反Wick算子的两项SzegIgn定理
Two-term Szegő theorem for generalised anti-Wick operators
摘要：
本文研究了一类伪微分算子的渐近性，其Weyl符号是一个被大尺度参数扩张的不连续函数与一个常尺度的光滑函数的卷积.这些算子包括作为特殊情况的广义反威克算子，也称为Gabor-Toeplitz算子，具有光滑窗口和扩张的不连续符号。主要结果是一个两项SzegIgn定理，即算子函数迹的渐近性。一个特殊情况是本征值计数函数的渐近项。在这两种情况下，以前只有渐近展开中的首项是明确已知的。
英文摘要：
This article concerns the asymptotics of pseudodifferential operators whose Weyl symbol is the convolution of a discontinuous function dilated by a large scaling parameter with a smooth function of constant scale. These operators include as a special case generalised anti-Wick operators, also known as Gabor-Toeplitz operators, with smooth windows and dilated discontinuous symbol. The main result is a two-term Szegő theorem, that is, the asymptotics of the trace of a function of the operator. A special case of this is the asymptotic terms of the eigenvalue counting function. In both cases, previously only the first term in the asymptotic expansion was known explicitly.
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