The aim of this note is to present a self-contained proof of the fact that a function can be approximated using a linear combination of Gaussian coherent states, with a number of terms controlled in terms of the smoothness and of the decay at infinity of the function. This result can easily be obtained using advanced results on modulation spaces, but the proof presented here is completely elementary and self-contained.

翻译：本文的目的是给出一个自包含的证明：一个函数可以使用高斯相干态的线性组合逼近，逼近所需的项数受到函数的平滑度和无穷远处的衰减的控制。这个结果可以很容易地使用调制空间的高级结果得到，但这里提供的证明完全是基础和自包含的。