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We introduce and study a new class of translation-modulation invariant Banachspaces of ultradistributions. These spaces show stability under Fouriertransform and tensor products; furthermore, they have a natural Banachconvolution module structure over a certain associated Beurling algebra, aswell as a Banach multiplication module structure over an associatedWiener-Beurling algebra. We also investigate a new class of modulation spaces,the Banach spaces of ultradistributions $\mathcal{M}^F$ on $\mathbb{R}^{d}$,associated to translation-modulation invariant Banach spaces ofultradistributions $F$ on $\mathbb{R}^{2d}$.

Translation-modulation invariant Banach spaces of ultradistributions