2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73009This paper is concerned with the characterization of $α$-modulation spaces by Banach frames, i.e., stable and redundant non-orthogonal expansions, constituted of functions obtained by a suitable combination of translation, modulation and dilation of a mother atom. In particular, the parameter $α\in [0,1]$ governs the dependence of the dilation factor on the frequency. The result is achieved by exploiting intrinsic properties of localization of such frames. The well-known Gabor and wavelet frames arise as special cases ($α= 0$) and limiting case ($ α\to 1)$, to characterize respectively modulation and Besov spaces. This intermediate theory contributes to a further answer to the theoretical need of a common interpretation and framework between Gabor and wavelet theory and to the construction of new tools for applications in time-frequency analysis, signal processing, and numerical analysis.24 pages, 1 figureFunctional Analysis42B35, 42C15, 46B25, 65T60text