5 citations · 15 across the 8 of their papers we have counts for
9 papers · 1 filter
Growth of Log-Analytic Functions
Tobias Kaiser
We show that unary log-analytic functions are polynomially bounded. In the higher dimensional case globally a log-analytic function can have exponential growth. We show that a log-…
Periods, Power Series, and Integrated Algebraic Numbers
Tobias Kaiser
Periods are defined as integrals of semialgebraic functions defined over the rationals. Periods form a countable ring not much is known about. Examples are given by taking the anti…
Differentiability Properties of Log-Analytic Functions
Tobias Kaiser, Andre Opris
We show that the derivative of a log-analytic function is log-analytic. We prove that log-analytic functions exhibit strong quasianalytic properties. We establish the parametric ve…
Ilyashenko algebras based on transserial asymptotic expansions
Zeinab Galal, Tobias Kaiser, Patrick Speissegger
We construct a Hardy field that contains Ilyashenko's class of germs at infinity of almost regular functions as well as all log-exp-analytic germs. In addition, each germ in this H…
Logarithms, constructible functions and integration on non-archimedean models of the theory of the real field with restricted analytic functions with value group of finite archimedean rank
Tobias Kaiser
Given a model of the theory of the real field with restricted analytic functions such that its value group has finite archimedean rank we show how one can extend the restricted log…
Analytic continuations of log-exp-analytic germs
Tobias Kaiser, Patrick Speissegger
We describe maximal, in a sense made precise, analytic continuations of germs at infinity of unary functions definable in the o-minimal structure R_an,exp on the Riemann surface of…