线性规划对偶在离散傅里叶分析和可加性问题中的应用
An application of linear programming duality to discrete Fourier analysis and additive problems
摘要：
假设f是一个来自Z_p -> [0，1]的函数（Z_p是我对整数mod p的表示法，而不是p-adics），并假设a_1，.，a_k是Z_p中的某些位置。在某些加性数论应用中，稍微扰动f，使得傅里叶变换f^在a_1，.处为零，a_k，而添加剂性质保持不变。在本文中，我们表明，即使我们在这方面是不成功的，我们至少可以说一些有趣的使用分离超平面，在线性规划对偶的基本成分的原则。
英文摘要：
Suppose that f is a function from Z_p -> [0,1] (Z_p is my notation for the integers mod p, not the p-adics), and suppose that a_1,...,a_k are some places in Z_p. In some additive number theory applications it would be nice to perturb f slightly so that Fourier transform f^ vanishes at a_1,...,a_k, while additive properties are left intact. In the present paper, we show that even if we are unsuccessful in this, we can at least say something interesting by using the principle of the separating hyperplane, a basic ingredient in linear programming duality.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
