6 problems

Let $X$ be the underlying space, let $\mathbb{F}$ be the scalar field, and let $K,Q:X^2\to\mathbb{F}$ be kernels. They are equivalent when, for every $r\geq 1$ and every…

Class-II self-similar-solution conjecture. A similar one-parameter family of self-similar solutions with finite mass should exist for nonsolvable class-II kernels, including one so…

The quartic oscillator Hamiltonian is the operator governing the eigenvalue problem for the quartic oscillator discussed in the paper. A simple and explicit kernel function is a ke…

Let $K(u,v)=\Phi(u+v)$, let $K_{[p]}$ be its compound kernel, and let $\phi_{[p]}$ and $\Lambda_{[p]}$ be the associated functions in the integral representation … Here…

Let $r>1$ be an order, and let $K(u,v;m)$ denote the kernel depending on the integer parameter $m$. Write $RR_r$ for the stated regularity class of kernels of order $r$. Compound-k…

Let $J$ be a convolution kernel, and consider the nonlocal heat equation with initial data whose growth is critical at the rate $|x|\ln|x|$. For gaussian kernels, Theorem 2 states…