2
votes
1answer
144 views

AM-GM interpolation in the limit

Given a sequence of positive numbers $X = (x_1, x_2, \dots)$, define the $k$th elementary symmetric mean of the first $n$ entries to be $$ S(X, n, k) := \frac{\displaystyle\sum_{1 \leq i_1 < ...
2
votes
2answers
290 views

L^2 basis of class functions on a compact Lie group that are point-wise small

Consider first the torus group $\mathbb{T}^k$. A natural $L^2$ basis is given by the 1-dimensional complex representations: $(\theta_1, \ldots, \theta_k) \mapsto e^{i \sum_j c_j \theta_j}$ for ...