Inverse spectral problem with partial information on the potential

Author: Khodakovsky, Andrei M.

Year: 1999

Degree: Dissertation (Ph.D.)

Advisor: Simon, Barry M.

Committee Member: Unknown, Unknown

Option: Mathematics

DOI: 10.7907/mkc2-dw32

Abstract

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.

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