Birinci Mertebeden Normal Diferansiyel Operatörlerin Bazı Sınıfları

Year 2023, , 356 - 362, 30.11.2023

Rukiye Öztürk Mert

https://doi.org/10.35193/bseufbd.1223029

Abstract

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.

Keywords

Normal Diferansiyel Operatör, Defekt Sayıları, Sınır Değer Uzayı, Spektrum

On Some Class of Normal Differential Operators for First Order

Abstract

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.

Keywords

Normal Differential Operator, Deficiency Indices, Space of Boundary Value, Spectrum

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