Embeddings of ultradistributions and periodic hyperfunctions in Colombeau type algebras through sequence spaces

2002/10/16 by Antoine Delcroix, Maximilian F. Hasler, Stevan Pilipović +1 · 1 citation
Arts and Humanities · Mathematics · #History and Theory of Mathematics #Mathematical and Theoretical Analysis #Philosophy and History of Science #math.FA #msc:46A45 #msc:46F30

paper · pdf · doi:10.1017/s0305004104007923

published as Math Proc Cambridge Phil Soc (2004), 137:3:697-708

arxiv created 2002/10/16 · openalex publication_date 2004/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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