Projects per year
Abstract
We consider a twodimensional analogue of Jacobi theta functions and prove that, among all lattices Λ⊂R2 with fixed density, the minimal value is maximized by the hexagonal lattice. This result can be interpreted as the dual of a 1988 result of Montgomery who proved that the hexagonal lattice minimizes the maximal values. Our inequality resolves a conjecture of Strohmer and Beaver about the operator norm of a certain type of frame in L2(R). It has implications for minimal energies of ionic crystals studied by Born, the geometry of completely monotone functions and a connection to the elusive Landau constant.
Original language  English 

Number of pages  62 
Publication status  Published  2021 
Austrian Fields of Science 2012
 101002 Analysis
 101032 Functional analysis
 103019 Mathematical physics
Keywords
 math.CA
 mathph
 math.FA
 math.MG
 math.MP
Activities
 2 Talk or oral contribution

Optimal sampling patterns in the timefrequency plane
Markus Faulhuber (Speaker)
10 Mar 2022Activity: Talks and presentations › Talk or oral contribution › Science to Science

Gaussian lattice sums
Markus Faulhuber (Speaker)
1 Dec 2021Activity: Talks and presentations › Talk or oral contribution › Science to Science