AI 中文总结
该研究在一维框架下引入含单参数的非局部能量，借助Cohn-Kumar普适性定理等方法，证明了此类能量的全局极小元为等间距粒子构型的周期基态。
AI 中文摘要
在一维情形下，我们引入一类含单参数的非局部能量，其中包括次临界Gagliardo半范数与Riesz泛函，作用于其导数为屏蔽狄拉克质量的周期构型的标量函数。我们证明了全局极小元由等间距的粒子构型给出，该结果通过将能量泛函表示为依赖于粒子间测地距离的相互作用势、利用这类势的完全单调性性质并借助著名的Cohn-Kumar普适性定理得到。
英文摘要
In dimension one, we introduce a one-parameter family of nonlocal energies, including subcritical Gagliardo seminorms and Riesz functionals, acting on scalar functions whose derivative is given by a periodic configuration of screened Dirac masses. We prove that the global minimizers are given by the equi-spaced configurations of particles. This result is achieved by representing the energy functionals as interaction potentials depending on the geodesic distances between the particles, exploiting the complete monotonicity properties of such potentials and invoking the celebrated Cohn-Kumar Universality Theorem.
