2013/11/13 by Piotr Nayar, Nayar, Piotr
Engineering · Mathematics · #42C10 #60E15 #Advanced Numerical Analysis Techniques #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #math.CO #msc:42C10 #msc:60E15
paper · pdf · doi:10.48550/arxiv.1311.3179
10 pages
arxiv created 2013/11/13 · openalex publication_date 2013/11/13 · arxiv updated 2013/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we consider Boolean functions defined on the discrete cube equipped with a biased product probability measure. We prove that if the spectrum of such a function is concentrated on the first two Fourier levels, then the function is close to a certain function of one variable. Moreover, in the symmetric case we prove that if a [-1,1]-valued function defined on the discrete cube is close to a certain affine function, then it is also close to a [-1,1]-valued affine function.