Boundary value and Wiener-Hopf problems for abstract kinetic equations with nonregular collision operators

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dc.contributor.authorGanchev, Alexander Hristoven
dc.contributor.committeechairGreenberg, W.en
dc.contributor.committeememberBall, J.A.en
dc.contributor.committeememberHagedorn, George A.en
dc.contributor.committeememberQuinn, F.en
dc.contributor.committeememberSlawny, J.en
dc.contributor.committeememberZweifel, Paul F.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-08-13T14:39:02Zen
dc.date.available2014-08-13T14:39:02Zen
dc.date.issued1986en
dc.description.abstractWe 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.en
dc.description.adminincomplete_metadataen
dc.description.degreePh. D.en
dc.format.extentv, 79 leavesen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/10919/50020en
dc.publisherVirginia Polytechnic Institute and State Universityen
dc.relation.isformatofOCLC# 14992786en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1986.G363en
dc.subject.lcshBoundary value problemsen
dc.subject.lcshWiener-Hopf equationsen
dc.titleBoundary value and Wiener-Hopf problems for abstract kinetic equations with nonregular collision operatorsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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