The L1-norm of exponential sums in d
2013 ◽
Vol 154
(3)
◽
pp. 381-392
◽
Keyword(s):
L1 Norm
◽
AbstractLet A be a finite set of integers and FA(x) = ∑a∈A exp(2πiax) be its exponential sum. McGehee, Pigno and Smith and Konyagin have independently proved that ∥FA∥1 ≥ c log|A| for some absolute constant c. The lower bound has the correct order of magnitude and was first conjectured by Littlewood. In this paper we present lower bounds on the L1-norm of exponential sums of sets in the d-dimensional grid d. We show that ∥FA∥1 is considerably larger than log|A| when A ⊂ d has multidimensional structure. We furthermore prove similar lower bounds for sets in , which in a technical sense are multidimensional and discuss their connection to an inverse result on the theorem of McGehee, Pigno and Smith and Konyagin.
2014 ◽
Vol 25
(07)
◽
pp. 877-896
◽
1998 ◽
Vol 50
(3)
◽
pp. 563-580
◽
2020 ◽
Vol 117
(28)
◽
pp. 16181-16186
Keyword(s):
2016 ◽
Vol 152
(7)
◽
pp. 1517-1554
◽
2003 ◽
Vol 40
(3)
◽
pp. 301-308
◽
2018 ◽
Vol 19
(4)
◽
pp. 1259-1286
Keyword(s):