Ganchev, Alexander Hristov2014-08-132014-08-131986http://hdl.handle.net/10919/50020We study the linear abstract kinetic equation T𝜑(x)′=-A𝜑(x) in the half space {x≥0} with partial range boundary conditions. The function <i>ψ</i> takes values in a Hilbert space H, T is a self adjoint injective operator on H and A is an accretive operator. The first step in the analysis of this boundary value problem is to show that T⁻¹A generates a holomorphic bisemigroup. We prove two theorems about perturbation of bisemigroups that are interesting in their own right. The second step is to obtain a special decomposition of H which is equivalent to a Wiener-Hopf factorization. The accretivity of A is crucial in this step. When A is of the form "identity plus a compact operator", we work in the original Hilbert space. For unbounded A’s we consider weak solutions in a larger space H_T, which has a natural Krein space structure. Using the Krein space geometry considerably simplifies the analysis of the question of unique solvability.v, 79 leavesapplication/pdfIn CopyrightLD5655.V856 1986.G363Boundary value problemsWiener-Hopf equationsDissertation