ESTIMATES FOR THE NUMBER OF EIGENVALUES OF NON-SELF-ADJOINT OPERATORS

1 online resource (85 pages) : PDF

2018

University of North Carolina at Charlotte

In this dissertation we find estimates for the total number of eigenvalues of non-self-adjoint operators. We consider five different operators, three of them discrete and two continuous. Discrete operators are as follows: Schrödinger operator defined on Z_+ with a complex potential, Schrödinger operator defined on Z with a complex potential, and a Dirac operator defined on Z, also with a complex potential. The latter of which we will also define in this dissertation, as, to the best of our knowledge, it has not yet been defined. Then we also consider a continuous Biharmonic operator on R^3 , and then a Polyharmonic operator of order 2l on R^d , both perturbed by a complex potential. For each of these operators we will find uniform bounds for the total number of eigenvalues located outside of their continuous spectrums. By‘uniform bounds’ we mean bounds which depend on the potential only through some simple quantities like L^p norms.

doctoral dissertations

Mathematics

Ph.D.

Dirac Operator
Discrete
Number of Eigenvalues
Polyharmonic Operator
Schroedinger Operator

Mathematics

Safronov, Oleg

Vainberg, Boris
McGoff, Kevin
Jacobs, Donald

Thesis (Ph.D.)--University of North Carolina at Charlotte, 2018.

This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). For additional information, see http://rightsstatements.org/page/InC/1.0/.

Copyright is held by the author unless otherwise indicated.

Hulko_uncc_0694D_11652

http://hdl.handle.net/20.500.13093/etd:769