1. CJM Online first
 Speissegger, Patrick

Quasianalytic Ilyashenko algebras
I 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 $\mathcal{F} \circ (\log)$ of germs at $0^+$ contains
all transition maps of hyperbolic saddles of planar real analytic
vector fields.
Keywords:generalized series expansion, quasianalyticity, transition map Categories:41A60, 30E15, 37D99, 03C99 

2. CJM 2006 (vol 58 pp. 1026)
 Handelman, David

Karamata Renewed and Local Limit Results
Connections between behaviour of real analytic functions (with no
negative Maclaurin series coefficients and radius of convergence one)
on the open unit interval, and to a lesser extent on arcs of the unit
circle, are explored, beginning with Karamata's approach. We develop
conditions under which the asymptotics of the coefficients are related
to the values of the function near $1$; specifically, $a(n)\sim
f(11/n)/ \alpha n$ (for some positive constant $\alpha$), where
$f(t)=\sum a(n)t^n$. In particular, if $F=\sum c(n) t^n$ where $c(n)
\geq 0$ and $\sum c(n)=1$, then $f$ defined as $(1F)^{1}$ (the
renewal or Green's function for $F$) satisfies this condition if $F'$
does (and a minor additional condition is satisfied). In come cases,
we can show that the absolute sum of the differences of consecutive
Maclaurin coefficients converges. We also investigate situations in
which less precise asymptotics are available.
Categories:30B10, 30E15, 41A60, 60J35, 05A16 

3. CJM 1999 (vol 51 pp. 117)