5 problems

Let $(X_n,d_n,\mu_n)$ for $n\in\mathbb{N}$ be a sequence of metric measure spaces that converges to $(X,d,\mu)$ in the Gromov–Wasserstein distance. The associated multidimensional…

For $n\geq 1$, let $\lambda_{n,3}$ denote the eigenvalue of the classical multidimensional-scaling kernel on $\mathbb{S}^2$ associated with spherical harmonics of degree $n$. Sign…

Let $n\geq 1$ be an integer, and let $\theta,\theta'\in\mathbb{S}^n$. The map $\Phi_{\mathbb{S}^n}$ is defined through the classical multidimensional scaling construction, and…

Let $(X,d,\mu)$ be a bounded metric measure space with kernel $K$ and associated operator $T_K\colon L^2(X,\mu)\to L^2(X,\mu)$. Let $(X,d,\mu_n)$ have analogous kernel $K_n$ and op…

Let $\a0p$ be odd. For the eigenvalues $\a0lambda_k(n)$ associated with the Fourier eigenvectors of the centered distance matrix for $n$ equally spaced points on the circle, let…