On convolved weight matrices and local solvability with controlled loss of regularity
arXiv:2607.28112
The paper defines a convolution operation for anisotropic weight matrices, studies its properties, shows how it alters associated Braun‑Meise‑Taylor weight functions, and uses it to analyze local solvability with controlled loss of regularity for a hyperbolic PDE.
Abstract
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.
27 pages