The Delsarte Method in the Problem of the Antipodal Contact Numbers of Euclidean Spaces of High Dimensions

Delsarte's Extremal Problem and Packing on Locally Compact Abelian Groups

Let G be a locally compact Abelian group, and let X, Y be two open sets in G. We investigate the extremal constant C(X,Y) defined to be the supremum of integrals of functions f from the class F(X,Y), where F(X,Y) is the family of positive definite functions f on G such that f(0) = 1, the positive part of f is supported in X, and its negative part is supported in Y. In the case when X=Y, the problem is exactly the so-called Turán problem for the set X. When Y= G, i.e., there is a restriction only on the set of positivity of f, we obtain the Delsarte problem. The Delsarte problem is the sharpest…

Turán问题与Delsarte问题及其对偶

The Turán and Delsarte problems and their duals

研究了欧氏空间正定函数的Turán和Delsarte优化问题，在连续情形下证明了对偶性质和极值子存在性，建立极值函数与对偶测度间的平移铺砌型关系，并证明非平移铺砌凸体的Delsarte堆积界严格优于体积堆积界。

Erdős–Falconer距离问题在有限域上的Delsarte线性规划方法

A Delsarte Linear Programming Approach to the Erdős--Falconer Distance Problem over Finite Fields

引入Delsarte线性规划方法，证明对偶维有限域上非退化二次型，当点集大小≥C q^{n/2+1/3}时，距离集包含正比例元素，改进了Iosevich–Rudnev的指数(n+1)/2至n/2+1/3。