Sequence spaces with exponent weights. Realizations of Colombeau type algebras
Volume 447 / 2007
Dissertationes Mathematicae 447 (2007), 1-56
MSC: Primary 46A45, 46F30;
Secondary
46E10, 46A03, 46A13, 46A50, 46E35,
46F05.
DOI: 10.4064/dm447-0-1
Abstract
We give a description of various algebras of generalized functions based on the introduction of pseudo-ultranorms on spaces of sequences in given locally convex function algebras. We study sheaf properties of these algebras, needed for microlocal analysis, and also consider regularity theory, functoriality and different concepts of association and weak equality in a unified setting. Using this approach, we also give new results on embeddings of ultradistribution and hyperfunction spaces into corresponding algebras of generalized functions.
