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Analytic Automorphisms and Transitivity of Analytic Mappings.
- Source :
-
Mathematics (2227-7390) . Dec2020, Vol. 8 Issue 12, p2179. 1p. - Publication Year :
- 2020
-
Abstract
- In this paper, we investigate analytic automorphisms of complex topological vector spaces and their applications to linear and nonlinear transitive operators. We constructed some examples of polynomial automorphisms that show that a natural analogue of the Jacobian Conjecture for infinite dimensional spaces is not true. Also, we prove that any separable Fréchet space supports a transitive analytic operator that is not a polynomial. We found some connections of analytic automorphisms and algebraic bases of symmetric polynomials and applications to hypercyclicity of composition operators. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 8
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 147804141
- Full Text :
- https://doi.org/10.3390/math8122179