Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 2458-7575 Bilecik Seyh Edebali University 10.35193/bseufbd.1223029 Numerical Analysis Pure Mathematics (Other) Sayısal Analiz Temel Matematik (Diğer) Birinci Mertebeden Normal Diferansiyel Operatörlerin Bazı Sınıfları On Some Class of Normal Differential Operators for First Order https://orcid.org/0000-0001-8083-5304 Öztürk Mert Rukiye HITIT UNIVERSITY 11 30 2023 10 2 356 362 12 22 2022 03 15 2023 Copyright © 2014, Bilecik Seyh Edebali University Journal of Science 2014 Bilecik Seyh Edebali University Journal of Science

Bu çalışmada, sonlu simetrik aralıktaki vektör fonksiyonların Hilbert uzayında, birinci mertebeden lineer diferansiyel-operatör ifadesi tarafından doğrulan minimal ve maksimal operatörleri oluşturulmuştur. Daha sonra, bu minimal operatörün defekt sayıları hesaplanmış ve sınır değer uzayı oluşturulmuştur. Calkin-Gorbachuk yöntemi kullanılarak, formal normal minimal operatörün tüm normal genişlemelerinin sınır değerler dilinde genel formu oluşturulmuştur. Son olarak, bu genişlemelerin spektrum yapısı araştırılmıştır.

In this work, we construct the minimal and maximal operators generated by linear differential-operator expression for first order in the Hilbert space of vector-functions on finite symmetric interval. Then, deficiency indices of the minimal operator will be calculated and the space of boundary values of this operator will be constructed. By using of Calkin-Gorbachuk method, the general representation of all normal extensions of the formally normal minimal operator in terms of boundary values will also be established. Moreover we explore the spectrum structure of these extensions.

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