Geodesic
Translation-invariant spaces of quasianalytic ultradistributions
Novi Sad Journal of Mathematics, Tome 45 (2015) no. 1.

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A class of translation-invariant Banach spaces of quasianalytic ultradistributions is introduced and studied. They are Banach modules over a Beurling algebra. Based on this class of Banach spaces, we define corresponding test function spaces $\mathcal{D}^*_E$ and their strong duals $\mathcal{D}'^*_{E'_{\ast}}$ of quasianalytic type, and study convolution and multiplicative products on $\mathcal{D}'^*_{E'_{\ast}}$. These new spaces generalize previous works about translation-invariant spaces of tempered (non-quasianalytic ultra-) distributions; in particular, our new considerations apply to the settings of Fourier hyperfunctions and ultrahyperfunctions. New weighted $\mathcal{D}'^{\ast}_{L^{p}_{\eta}}$ spaces of quasianalytic ultradistributions are analyzed.
Publié le :
DOI : 10.30755/NSJOM.dans14.07
Classification : 46F05, 46H25, 46F10, 46F15, 46E10
Keywords: Quasianalytic ultradistributions, Convolution of ultradistributions, Translation-invariant Banach space of ultradistributions, Tempered ultradistributions, Beurling algebra, Hyperfunctions 
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Pavel Dimovski; Bojan Prangoski; Jasson Vindas. Translation-invariant spaces of quasianalytic ultradistributions. Novi Sad Journal of Mathematics, Tome 45 (2015) no. 1. doi : 10.30755/NSJOM.dans14.07. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.dans14.07/

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