We obtain estimates for the $L^p$-norm of the short-time Fourier transform (STFT) for functions in modulation spaces, providing information about the concentration on a given subset of ${\mathbb{R}}^2$, leading to deterministic guarantees for perfect reconstruction using convex optimization methods. More precisely, we obtain large sieve inequalities of the Donoho-Logan type, but instead of localizing the signals in regions $T\times W$ of the time-frequency plane using the Fourier transform to intertwine time and frequency, we localize the representation of the signals in terms of the short-time Fourier transform in sets Δ with arbitrary geometry. At the technical level, since there is no proper analogue of Beurling's extremal function in the STFT setting, we introduce a new method, which rests on a combination of an argument similar to Schur's test with an extension of Seip's local reproducing formula to general Hermite windows. When the windows are Hermite functions, we obtain local reproducing formulas for polyanalytic Fock spaces which lead to explicit large sieve constant estimates and, as a byproduct, to a reconstruction formula for $f\in L^2(\mathbb{R})$ from its STFT values on arbitrary discs.

我们获得估计 ${升}^{磷}$-调制空间中函数的短时傅立叶变换 (STFT)范数，提供关于给定子集的浓度的信息${\mathbb{电阻}}^2$，导致使用凸优化方法完美重建的确定性保证。更准确地说，我们获得了 Donoho-Logan 类型的大筛子不等式，但不是在区域中定位信号$吨\times 宽$使用傅立叶变换来交织时间和频率的时频平面，我们根据短时傅立叶变换在具有任意几何形状的集合 Δ 中定位信号的表示。在技​​术层面，由于在 STFT 设置中没有 Beurling 极值函数的适当类比，我们引入了一种新方法，该方法依赖于类似于 Schur 检验的论证与将 Seip 的局部再现公式扩展到一般 Hermite 窗口的组合. 当窗口是 Hermite 函数时，我们获得了多分析 Fock 空间的局部再现公式，这导致显式的大筛常数估计，并且作为副产品，得到了一个重建公式$F\in {升}^2(\mathbb{电阻})$ 从其在任意光盘上的 STFT 值。