We 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<sub>T</sub>, which has a natural Krein space structure. Using the Krein space geometry considerably simplifies the analysis of the question of unique solvability. / Ph. D. / incomplete_metadata
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/50020 |
| Date | January 1986 |
| Creators | Ganchev, Alexander Hristov |
| Contributors | Mathematics, Greenberg, W., Ball, J.A., Hagedorn, George A., Quinn, F., Slawny, J., Zweifel, Paul F. |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | v, 79 leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 14992786 |
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