TY  - JOUR
T1  - A Study on the Non-selfadjoint Schrödinger Operator with Negative Density Function
TT  - Negatif Yoğunluk Fonksiyonuna Sahip Kendine Eşlenik Olmayan Schrödinger Operatörü Üzerine Bir Çalışma
AU  - Coskun, Nimet
PY  - 2023
DA  - April
DO  - 10.53433/yyufbed.1139044
JF  - Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi
JO  - YYU JINAS
PB  - Van Yüzüncü Yıl Üniversitesi
WT  - DergiPark
SN  - 1300-5413
SP  - 220
EP  - 229
VL  - 28
IS  - 1
LA  - en
AB  - This study focuses on the spectral features of the non-selfadjoint singular operator with an out-of-the-ordinary type weight function. Take into consideration the one-dimensional time-dependent Schrödinger type differential equation-y^''+q(x)y=μ^2 ρ(x)y,x∈[0,∞),holding the initial conditiony(0)=0,and the density function defined with a completely negative value asρ(x)=-1.There is an enormous number of the papers considering the positive values of ρ(x) for both continuous and discontinuous cases. The structure of the density function affects the analytical properties and representations of the solutions of the equation. Unlike the classical literature, we use the hyperbolic type representations of the equation’s fundamental solutions to obtain the operator’s spectrum. Additionally, the requirements for finiteness of eigenvalues and spectral singularities are addressed. Hence, Naimark’s and Pavlov’s conditions are adopted for the negative density function case.
KW  - Negative density function
KW  - Spectral analysis
KW  - Spectral singularities
N2  - Bu çalışmada kendine eşlenik olmayan, singüler ve standard dışı bir ağırlık fonksiyonuyla birlikte tanımlanmış operatörün spektral özellikleri ele alınacaktır. Bir boyutlu, zamana bağımlı Schrödinger tipli diferansiyel denklem-y^''+q(x)y=μ^2 ρ(x)y,x∈[0,∞),y(0)=0,başlangıç koşulu ve tamamen negatif olarak tanımlıρ(x)=-1,yoğunluk fonksiyonuyla birlikte göz önüne alınsın. Pozitif değerli sürekli ve süreksiz yoğunluk fonksiyonuna sahip operatörler için literatürde çok sayıda çalışma bulunmaktadır. Yoğunluk fonksiyonunun yapısı operatörün analitik özelliklerini ve çözümlerin gösterimini etkilemektedir. Klasik literatürden farklı olarak, bu çalışmada hiperbolik tipli temel çözümler operatörün spektrumunu belirlemek için kullanılmıştır. Buna ek olarak, özdeğerlerin ve spektral tekilliklerin sonluluğu için gerekli koşullar elde edilmiştir. Böylece, Naimark ve Pavlov koşulları, negatif yoğunluk fonksiyonuna sahip operatör durumunda çözülmüştür.
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UR  - https://doi.org/10.53433/yyufbed.1139044
L1  - https://dergipark.org.tr/tr/download/article-file/2519508
ER  -