2026/07/30 by Gerhard Schindl
Mathematics · #math.FA #math.AP #msc:26A12 #msc:26A48 #msc:35K65 #msc:46E05 #msc:46E10
27 pages
arxiv created 2026/07/30 · arxiv updated 2026/07/31
We introduce the convolution between abstractly given anisotropic weight matrices and investigate properties of this new construction. Further, we apply the knowledge to the particular but interesting case when the (isotropic) matrices are associated with weight functions in the sense of Braun-Meise-Taylor and show how the convolution of associated weight matrices modifies the underlying weight functions. Finally, we give a concrete application of the convolution when studying the concept of local solvability for a certain hyperbolic PDE. Indeed, the convolution allows to treat in a natural way a mixed setting; i.e. having a controlled loss of regularity expressed in terms of two, in general different, weight sequences.