2 results
Multisummability for generalized power series
- Part of
-
- Journal:
- Canadian Journal of Mathematics / Volume 76 / Issue 2 / April 2024
- Published online by Cambridge University Press:
- 27 February 2023, pp. 458-494
- Print publication:
- April 2024
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
We develop multisummability, in the positive real direction, for generalized power series with natural support, and we prove o-minimality of the expansion of the real field by all multisums of these series. This resulting structure expands both
$\mathbb {R}_{\mathcal {G}}$ and the reduct of 
$\mathbb {R}_{\text {an}^*}$ generated by all convergent generalized power series with natural support; in particular, its expansion by the exponential function defines both the gamma function on 
$(0,\infty )$ and the zeta function on 
$(1,\infty )$.
Quasianalytic Ilyashenko Algebras
-
- Journal:
- Canadian Journal of Mathematics / Volume 70 / Issue 1 / 01 February 2018
- Published online by Cambridge University Press:
- 20 November 2018, pp. 218-240
- Print publication:
- 01 February 2018
-
- Article
-
- You have access
- Export citation
-
We construct a quasianalytic field
$\mathcal{F}$ of germs at 
$+\infty $ of real functions with logarithmic generalized power series as asymptotic expansions, such that $\mathcal{F}$ is closed under differentiation and log-composition; in particular, $\mathcal{F}$ is a Hardy field. Moreover, the field 
$\mathcal{F}\,\circ \,\left( -\text{log} \right)$ of germs at 
${{0}^{+}}$ contains all transition maps of hyperbolic saddles of planar real analytic vector fields.
