arXiv subjects
Publications and source records attributed to Vincent Valmorin.
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove functorial properties of those algebras and show how weak equalities, in the sense of various associations, can be described in this setting.
In a recent paper, we gave a topological description of Colombeau type algebras introducing algebras of sequences with exponential weights. Embeddings of Schwartz' spaces into the Colombeau algebra G are well known, but for ultradistribution and periodic hyperfunction type spaces we give new constructions. We show that the multiplication of regular enough functions (smooth, ultradifferentiable or quasianalytic), embedded into corresponding algebras, is the ordinary multiplication.
A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of exponential weights. Such an algebra with embedded Dirac's delta distribution induces discrete topology on the basic space. This result is in analogy to Schwartz' impossibility result concerning multiplication of distributions.