Abstract
In this paper, we construct new nonstandard hulls of topological vector spaces using convex subrings of∗ R (or∗ C) and we show that such spaces are complete. Some examples of locally convex spaces are provided to illustrate our construction. Namely, we show that the new nonstandard hull of the space of polynomials is the algebra of Colombeau’s entire holomorphic generalized functions. The proof is based on the existence of global representatives of entire generalized functions.
| Original language | English |
|---|---|
| Pages (from-to) | 2723-2739 |
| Number of pages | 17 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 146 |
| Issue number | 6 |
| DOIs | |
| State | Published - 2018 |
Bibliographical note
Publisher Copyright:© 2018 Amerian Mathematial Soiety.
Keywords
- Generalized holomorphicity
- Internal polynomials
- Nonstandard analysis
- Nonstandard hulls
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics