关于微分中间值性质

IF 0.6 4区数学 Q3 MATHEMATICS

Revista De La Union Matematica Argentina Pub Date : 2021-05-26 DOI:10.33044/revuma.2892

Matthias Aschenbrenner, L. Dries, J. Hoeven

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引用次数: 0

摘要

Liouville闭h场是一种有序的微分场，它的序和导数以一种自然的方式相互作用，其中每一个1阶的线性微分方程都有一个非平凡解。(引言给出了一个精确的定义。)对于具有小导数的Liouville闭h域K，我们证明了:如果K初等等价于横列的有序微分域，则K具有微分多项式的中间值性质。我们还指出这如何适用于哈迪领域。

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On a differential intermediate value property

Liouville closed H-fields are ordered differential fields whose ordering and derivation interact in a natural way and where every linear differential equation of order 1 has a nontrivial solution. (The introduction gives a precise definition.) For a Liouville closed H-field K with small derivation we show: K has the Intermediate Value Property for differential polynomials iff K is elementarily equivalent to the ordered differential field of transseries. We also indicate how this applies to Hardy fields.

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来源期刊

Revista De La Union Matematica Argentina MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Revista de la Unión Matemática Argentina is an open access journal, free of charge for both authors and readers. We publish original research articles in all areas of pure and applied mathematics.