Convergence results for function spaces over o-minimal structures
نویسندگان
چکیده
منابع مشابه
Convergence results for function spaces over o-minimal structures
We begin the development of a theory of Banach spaces in the definable setting of o-minimal structures. We outline several results which develop the theory of compact embeddings for explicitly given function spaces. One aim is to explain the substantive underpinnings of an important observation used in the proof of the Reparameterization Theorem of Pila and Wilkie in [2]. We place this observat...
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R l definable in R such that F (t) = G(t, F (t)) for all t ∈ (a, b) and each component function Gi : R 1+l → R is independent of the last l− i variables (i = 1, . . . , l). If R is o-minimal and F : (a, b) → R is R-Pfaffian, then (R, F ) is o-minimal (Proposition 7). We say that F : R → R is ultimately R-Pfaffian if there exists r ∈ R such that the restriction F ↾(r,∞) is R-Pfaffian. (In genera...
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We investigate the asymptotic behavior at +∞ of non-oscillatory solutions to differential equations y′ = G(t, y), t > a, where G : R1+l → Rl is definable in a polynomially bounded o-minimal structure. In particular, we show that the Pfaffian closure of a polynomially bounded o-minimal structure on the real field is levelled. A classical topic in asymptotic analysis is the study of the behavior ...
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ژورنال
عنوان ژورنال: Journal of Logic and Analysis
سال: 2012
ISSN: 1759-9008
DOI: 10.4115/jla.2012.4.1