短时傅里叶变换中浓度算子的谱偏差
Spectral deviation of concentration operators for the short-time Fourier transform
AI总结：
该研究针对短时傅里叶变换的时频浓度算子，估计其特征值计数函数与勒贝格测度的偏差，给出Gelfand-Shilov类窗函数的有效界，并考虑多项式衰减窗函数，支持相关几何依赖场景的应用。
摘要：
时频浓度算子将短时傅里叶变换的积分分析-合成公式限制在给定的紧域上。我们估计了相应的特征值计数函数与时频域勒贝格测度的偏差程度。对于Gelfand-Shilov类窗函数，所得界几乎与已知渐近结果一致，其优势在于对具体域和谱阈值均有效。因此，我们的估计可应用于谱阈值依赖于时频浓度域几何结构的场景。我们还考虑了仅在时间和频率上呈多项式衰减的窗函数。
英文摘要：
Time-frequency concentration operators restrict the integral analysis-synthesis formula for the short-time Fourier transform to a given compact domain. We estimate how much the corresponding eigenvalue counting function deviates from the Lebesgue measure of the time-frequency domain. For window functions in the Gelfand-Shilov class, the bounds almost match known asymptotics, with the advantage of being effective for concrete domains and spectral thresholds. As such our estimates allow for applications where the spectral threshold depends on the geometry of the time-frequency concentration domain. We also consider window functions that decay only polynomially in time and frequency.
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