Wiener's problem for positive definite functions

作者：Gorbachev D. V.^*; Tikhonov S. Yu.

来源：Mathematische Zeitschrift, 2018, 289(3-4): 859-874.

DOI：10.1007/s00209-017-1978-9

• Positive definite function
• Wiener's problem
• Hlawka's inequality
• Sharp constant
• Linear programming bound problem

We study the sharp constant in Wiener's inequality for positive definite functions
Tn | f | 2 dx = Wn( D)| D|- 1 D | f | 2 dx, D. Tn
Wiener proved that , . Hlawka showed that , where D is an origin-symmetric convex body. We sharpen Hlawka's estimates for D being the ball and the cube . In particular, we prove that . We also obtain a lower bound of . Moreover, for a cube with we obtain that . Our proofs are based on the interrelation between Wiener's problem and the problems of Turan and Delsarte.

• 出版日期2018-8