Inversion formulas for the short-time Fourier transform

The inversion formula for the short-time Fourier transform is usually considered in the weak sense, or only for specific combinations of window functions and function spaces such as L2. In the present article the so-called θ-summability (with a function parameter θ) is considered which induces norm convergence for a large class of function spaces. Under some conditions on θ we prove that the summation of the short-time Fourier transform of ƒ converges to ƒ in Wiener amalgam norms, hence also in the Lp sense for Lp functions, and pointwise almost everywhere.