On the Determination of the Singular Sturm-Liouville Operator from Two Spectra


Panakhov E. S. , SAT M.

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, cilt.84, ss.1-11, 2012 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 84 Konu: 1
  • Basım Tarihi: 2012
  • Dergi Adı: CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
  • Sayfa Sayıları: ss.1-11

Özet

In this paper an inverse problem by two given spectrum for a second-order differential operator with coulomb singularity of the type A/x in zero point (here A is constant), is studied. It is well known that two spectrum {lambda(n)} and {mu(n)} uniquely determine the potential function q(x) in the singular Sturm-Liouville equation defined on interval (0,pi]. The aim of this paper is to prove the generalized degeneracy of the kernel K(x,t). In particular, we obtain a new proof of the Hochstadt's theorem concerning the structure of the difference (q) over tilde (x) - q(x).