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Title:The field of reals with Gevrey functions is model complete and o-minimal
Author(s):Speissegger, Patrick Urs
Doctoral Committee Chair(s):van den Dries, Lou
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Mathematics
Abstract:Infinitely representable functions are introduced, and it is proved that the expansion $\IR\sb{\cal G}$ of the field of reals by a certain subfamily of all infinitely representable functions (namely, the family of so-called Gevrey functions) is model complete and o-minimal as well as polynomially bounded. The function $\phi$ given on (1, $\infty$) by$$\log\Gamma(x)=\left(x-{1\over2}\right)\log x-x+{1\over2}\log(2\pi)+\phi(x)$$is definable in $\IR\sb{\cal G},$ as are all functions whose Taylor series expansion at the origin is multisummable in the direction $\IR\sp+$.
The class of all infinitely representable functions is shown to be the same as the class of all finite sums of functions satisfying Gevrey estimates on disks (rather than on sectors of large enough opening). This leads to a generalization of the theory of multisummability in the direction $\IR\sp+$. An example of an infinitely representable function whose Taylor series is not multisummable in the direction $\IR\sp+$ is constructed.
Issue Date:1996
Type:Text
Language:English
URI:http://hdl.handle.net/2142/22842
ISBN:9780591200003
Rights Information:Copyright 1996 Speissegger, Patrick Urs
Date Available in IDEALS:2011-05-07
Identifier in Online Catalog:AAI9712443
OCLC Identifier:(UMI)AAI9712443


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