Daniel J. Miller
Characterizing decidability in a quasianalytic setting.
Wed, 08/18/2010 - 15:01 — SomNambulAuthors: Daniel J. Miller
Subjects: Logic
AbstractLet $\RR_S$ denote the expansion of the real ordered field by a family of
real-valued functions $S$, where each function in $S$ is defined on a compact
box and is a member of some quasianalytic class which is closed under the
operations of function composition, division by variables, and implicitly
defined functions. It is shown that the first order theory of $\RR_S$ is
decidable if and only if two oracles, called the approximation and precision
oracles for $S$, are decidable.Stability under integration of sums of products of real globally subanalytic functions and their logarithms.
Tue, 11/24/2009 - 16:01 — SomNambulAuthors: Raf Cluckers, Daniel J. Miller
Subjects: Algebraic Geometry
AbstractWe study Lebesgue integration of sums of products of globally subanalytic
functions and their logarithms, called constructible functions. Our first
theorem states that the class of constructible functions is stable under
integration. The second theorem treats integrability conditions in Fubini-type
settings, and the third result gives decay rates at infinity for constructible
functions. Further, we give preparation results for constructible functions
related to integrability conditions.
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