5 papers · 1 filter
An Bohnenblust--Hille Bound on the Boolean Cube
Joseph Slote, Chun-Kai Tseng, Alexander Volberg
Let and put \[ β_0=\frac{3}{2}+\frac{1}{\log 2}=2.9426950408\ldots, \] where is the natural logarithm. We give a proof scheme showing that, for every $\vareps…
Polynomial Bohnenblust--Hille bounds for product of cyclic groups
Joseph Slote, Alexander Volberg
Fix an integer , and let be the product of cyclic groups of order . For a Fourier character , let be the numbe…
Tightness of and counterexamples to several quantum estimates
Joseph Slote, Alexander Volberg, Haonan Zhang
We prove here several tightness results for such quantum inequalities as 1) the comparison of operator norm and product norm of -local hamiltonians, 2) Bohnenblust--Hille inequa…
Small moments of the sensitivity of polynomial threshold functions
Chun-Kai Tseng, Alexander Volberg
In the first version of Chang, Slote, Volberg, and Zhang's paper \cite{BSA_of_PTF}, the authors modify a nice recursive approach due to Kane in \cite{Correct_exponent_for_AS} where…
The estimates for Boolean surface area of polynomial threshold functions
Fan Chang, Joseph Slote, Alexander Volberg +2
Polynomial threshold functions (PTFs) are an important low-complexity class of Boolean functions, with strong connections to learning theory and approximation theory. Recent work o…