Topics in spectral theory of differential operators /

This dissertation is devoted to two eigenvalue counting problems: Determining the asymptotic behavior of large eigenvalues of self-adjoint extensions of partial differential operators, and computing the number of negative eigenvalues for bounded from below operators with compact resolvents. In the first part of this thesis we derive a Weyl-type asymptotic formula and a bound for the eigenvalue counting function for the Krein-von Neumann extension of differential operators on open bounded subsets of R n. In the second part of this thesis we obtain a formula relating the Maslov index, a topological invariant counting the signed number of conjugate points of paths of Lagrangian planes in H1/2 ([boundary symbol]) x H-1/2 ([boundary symbol]) and the Morse index, the number of negative eigenvalues, for the second order differential operators with domains of definition contained in H1 ([omega]) for open bounded subsets [omega] [symbol] R[subscript n].

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics (MU)

Grantor dc:publisher

University of Missouri--Columbia

Year dc:date.issued

2017

Author dc:creator

• Sukhtaiev, Selim, 1990-

Advisors dc:contributor.advisor

• Gesztesy, Fritz, 1953-
• Latushkin, Yuri, 1956-

Statement dc:rights

• OpenAccess.

Language dc:language.iso

eng, English

Handle dc:identifier.uri

https://hdl.handle.net/10355/62261

OAI identifier oai:identifier

oai:mospace.umsystem.edu:10355/62261