Dimension-Free Estimates for Low Degree Functions on the Hamming Cube

Explore dimension-free L^p inequalities for low degree scalar-valued functions on the Hamming cube in this 1-hour 5-minute lecture. Delve into Bernstein-Markov type inequalities for functions with spectrum bounded from above, examining cases for p>2 and p∈(1,2). Discover corollaries for Boolean-valued and ternary functions, emphasizing dimension-independent constants. Investigate counterparts of these results on tail spaces. Learn about the collaborative research stemming from the "Analysis on the hypercube with applications to quantum computing" workshop at the American Institute of Mathematics.