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Inverse spectral problem with partial information on the potential


Khodakovsky, Andrei M. (1999) Inverse spectral problem with partial information on the potential. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/mkc2-dw32.


NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

The Schrodinger operator [...] is considered on the real axis. We discuss the inverse spectral problem where discrete spectrum and the potential on the positive half-axis determine the potential completely. We do not impose any restrictions on the growth of the potential but only assume that the operator is bounded from below, has discrete spectrum, and the potential obeys [...]. Under these assertions we prove that the potential for [...] and the spectrum of the problem uniquely determine the potential on the whole real axis. Also, we study the uniqueness under slightly different conditions on the potential. The method employed uses Weyl m-function techniques and asymptotic behavior of the Herglotz functions.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Simon, Barry M.
Thesis Committee:
  • Unknown, Unknown
Defense Date:19 May 1999
Record Number:CaltechETD:etd-09072005-131144
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3372
Deposited By: Imported from ETD-db
Deposited On:12 Sep 2005
Last Modified:19 Apr 2021 22:38

Thesis Files

PDF (Khodakovsky_am_1999.pdf) - Final Version
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