Positivity of the difference neutron transport operator

In the present study, a two-dimensional difference neutron transport operator is considered. The resolvent equation for this neutron transport operator is constructed. The positivity of this difference neutron transport operator in (Formula presented) is provided. The structure of fractional spaces generated by the two-dimensional difference neutron transport operator is studied. It is established that the norms in the spaces (Formula presented) and (Formula presented) are equivalent. This result enabled us to prove the positivity of the difference neutron transport operator in the Slobodeckij space. In practice, the theorem on the stability of the Cauchy problem for the difference neutron transport equation in Banach spaces is presented. © 2021 Academic Publications