Herglotz-Nevanlinna Fonksiyonu İçeren Sınır Koşullarına Sahip Dirac Operatörü için Ters Problemler

Yıl 2017, Cilt: 38 Sayı: 2, 204 - 218, 24.04.2017

Yalçın Güldü A. Sinan Özkan

https://doi.org/10.17776/cumuscij.308486

Öz

Bu makalede, sınır koşulları spektral
parametreye rasyonel, süreksizlik koşulları ise lineer şekilde bağlı olan Dirac
operatörü için ters problem ele alınmıştır. (½,1) aralığında Q(x) potansiyel
fonksiyonu biliniyorken, tek spektrumun sonlu sayıda özdeğerlerin dışında (0,1)
aralığında Q(x) potansiyel fonksiyonunu ve problemin diğer katsayılarını tek
olarak belirlediği ispatlanmaktadır. Ayrıca, Q(x) fonksiyonunun klasik spektral
veriler, yani özdeğerler ve normalleştirici sayılar yardımıyla tek olarak
belirlendiği gösterilmektedir.

Anahtar Kelimeler

Ters problem, süreksiz Dirac operatör, sınır-değer problem

Inverse Problems for Dirac Operator with Boundary Conditions İnvolving A Herglotz-Nevanlinna function

Öz

In this paper, we deal with the inverse problems for
Dirac operator with rationally eigenvalue dependent boundary condition and
linearly eigenvalue dependent jump conditions. We prove that when  is known on  then only one spectrum
excluding a finite number of eigenvalues is sufficient to determine  on the interval  and the other
coefficients of the problem. Moreover, it is shown that  is uniquely determined
by the classical spectral data, i.e., eigenvalues and normalising numbers.

Anahtar Kelimeler

Inverse problem, impulsive differential equation, boundary value problem

Kaynakça

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