On commutativity of unbounded operators in Hilbert spaceTheses and Dissertations
Date of Degree2011
Degree NamePhD (Doctor of Philosophy)
First AdvisorPalle Jorgensen
AbstractWe study several unbounded operators with view to extending von Neumann's theory of deficiency indices for single Hermitian operators with dense domain in Hilbert space. If the operators are non-commuting, the problems are difficult, but special cases may be understood with the use representation theory. We will further study the partial derivative operators in the coordinate directions on the L2 space on various covering surfaces of the punctured plane. The operators are defined on the common dense domain of C∞ functions with compact support, and they separately are essentially selfadjoint, but the unique selfadjoint extensions will be non-commuting. This problem is of a geometric flavor, and we study an index formulation for its solution. The applications include the study of vector fields, the theory of Dirichlet problems for second order partial differential operators (PDOs), Sturm-Liouville problems, H.Weyl's limit-point/limit-circle theory, Schrödinger equations, and more.
- index theory,
- point interaction,
- Schrödinger equations,
- self-adjoint extension,
Pagesvi, 117 pages
BibliographyIncludes bibliographical references (pages 113-117).
CopyrightCopyright 2011 Feng Tian
Citation InformationFeng Tian. "On commutativity of unbounded operators in Hilbert space" (2011)
Available at: http://works.bepress.com/feng_tian/2/