Title
Spectral Theory of Speed-One Neutron Transport Operators
Abstract
We calculate the essential spectra of speed-one neutron transport operators of the form $i\mu\partial_x+i\sigma(x)-C(x)\int_{[-1,1]}k(\mu,\nu)\cdot d\nu$ in the space $L^2(\mathbf{R}_x\times [-1,1]_\mu)$. To this end, we construct singular Weyl sequences for $i\mu\partial_x+i\sigma(x)$ and apply a compactness criterion for integral operators to obtain a description of the essential spectrum of $i\mu\partial_x+i\sigma(x)-C(x)\int_{[-1,1]}k(\mu,\nu)\cdot d\nu$ under suitable conditions on $C$ and $k$.