Spectral Theory Problems on Graphs and Their Applications
Typ dokumentu
habilitační prácehabilitation thesis
Autor
Lipovský, Jiří
Metadata
Zobrazit celý záznamAbstrakt
The present habilitation thesis is a collection of nine papers in spectral theory.
Several models are used, namely, quantum graphs, microwave networks, damped
wave equation, and the polyharmonic operator. The operators used in the thesis
act on metric graphs; both compact and open graphs are used. Spectral prop erties of quantum graphs with preferred-orientation coupling are obtained, the
Gelfand-Levitan trace formula is found for quantum graphs with generic cou pling conditions, and resonance properties of open quantum graphs are investi gated. The results on quantum graphs are verified in two papers on microwave
networks’ experiments. Asymptotic spectral properties of the damped wave equa tion on graphs and the spectral determinant for the polyharmonic operator are
investigated.
Kolekce
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