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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.<\/jats:p>","DOI":"10.1007\/s11565-026-00763-9","type":"journal-article","created":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T06:04:12Z","timestamp":1790661852000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On convolved weight matrices and local solvability with controlled loss of regularity"],"prefix":"10.1007","volume":"72","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2192-9110","authenticated-orcid":false,"given":"Gerhard","family":"Schindl","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,9,29]]},"reference":[{"issue":"1","key":"763_CR1","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1007\/s43037-020-00090-x","volume":"15","author":"C Boiti","year":"2021","unstructured":"Boiti, C., Jornet, D., Oliaro, A., Schindl, G.: Nuclear global spaces of ultradifferentiable functions in the matrix weighted setting. 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