Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers-Loeser in the context of semi-algebraic and sub-analytic structures, when they studied stability under integration. In this paper we will present a natural refinement of their definition that allows for stability results to hold within the wider class of P-minimal structures. One of the main technical improvements is that we remove the requirement of definable Skolem functions from the proofs. As a result, we obtain stability in particular for all intermediate structures between the semi-algebraic and the sub-analytic languages.
Local integrability results in harmonic analysis on reductive groups in large positive characteristic
设$G$是非阿基米德局部域$K$上的连通约化代数群，$g$是它的李代数.利用Harish-Chandra定理，若$K$具有特征零点，则轨道积分的傅里叶变换在$g(K)$的正则元集上用局部常数函数表示，且该函数通过零点推广到所有$g(K)$，是局部可积的.在本文中，我们证明了这些函数实际上是可构造的motivic指数函数的特殊化。结合可积性的转移原理[R. Cluckers，J. Gordon，I. Halupczok，“Transfer principles for integrability and boundedness conditions for motivic指数函数“，preprint arXiv：1111.4405]，我们得到Harish-Chandra定理在$K$是具有充分大正特征的非阿基米德局部场时也成立。在伪指数映射存在的假设下，这也意味着$G(K)$的容许表示的Harish-Chandra特征标的局部可积性，其中$K$是一个具有足够大（依赖于$G$的根数据）特征的等特征域.
