#### Çankaya University Mathematics Department Seminars

The Spectral Analysis of Dissipative Operators
Elgiz Bayram
Ankara Üniversitesi, Turkey
Özet : Let $L_{\min }$ denote the minimal symmetric operator in $L_{2}(0,\infty )$ generated by the differential expression $\ell (y):=-\left( p(x)y^{\prime }\right) ^{\prime }+q(x)y,\text{ }x\in \lbrack 0,\infty ).$% We assume that the deficiency indices of $L_{\min }$ are $(2,2).$ In other words, we assume that the differential expression $\ell (y)$ is in limit-circle case. In this talk, using Livsic's theorem and Krein's theorem we prove that the root vectors (principle vectors) associated with the discrete spectrum of the maximal dissipative extensions of the minimal symmetric operator $L_{\min }$ are complete in $L_{2}(0,\infty ).$ Moreover, we show that this method can also be generalized to some dissipative operators with transmission (impulsive) conditions.
 Tarih : 06.11.2015 Saat : 13:20 Yer : Çankaya Üniversitesi R-213 Dil : English Ek Dosya : Özet