4 citations · 11 across the 11 of their papers we have counts for
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Definability of complex functions in o-minimal structures
Adele Padgett, Patrick Speissegger
We prove that some holomorphic continuations of functions in the classes and are definable in the o-minimal structures an…
Transasymptotic expansions of o-minimal germs
Jean-Philippe Rolin, Tamara Servi, Patrick Speissegger
Given an o-minimal expansion of the real ordered field, generated by a generalized quasianalytic class , we construct an explicit truncation…
Expansions of the real field by canonical products
Chris Miller, Patrick Speissegger
We consider expansions of o-minimal structures on the real field by collections of restrictions to the positive real line of the canonical Weierstrass products associated to sequen…
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…
Limit cycles of planar vector fields: Hilbert's 16th problem and o-minimality
Patrick Speissegger
I discuss some recent work linking certain aspects of the second part of Hilbert's 16th problem to the theory of \hbox{o-minimality}. These notes are adapted from a lecture I gave…
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…