5 problems

Condition-number monotonicity conjecture. For the Gaussian or inverse multiquadric RBF,

Generalized native-space inclusion conjecture. The native space $\mathcal{N}_G^{\mathscr{P}}(\mathbb{R}^2)$ associated with $G$ and $\mathscr{P}$ is a subspace of…

Let $\Xi$ be a quasiuniform subset of $SO(3)$ with mesh ratio $\rho$. For the kernel $k_m$ on $SO(3)$ and its associated space $S(k_m,\Xi)$, let $\chi_{\xi}$ denote the Lagrange fu…

Let $\Xi$ be a quasiuniform center set with mesh ratio $\rho$, and let $\phi_{\beta}=G_{\beta}+G_{\beta}*\psi$ with $\beta>d$. Let $S(\phi_{\beta},\Xi)$ be the associated kernel sp…

Let $\Xi$ be a quasiuniform set of centers on the sphere, with mesh ratio $\rho$. For restricted surface splines $\varphi_m$ and the associated conditionally positive-definite kern…