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Dergiler / Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi / 2023 / Cilt: 10 Sayı: 2

Birinci Mertebeden Normal Diferansiyel Operatörlerin Bazı Sınıfları

On Some Class of Normal Differential Operators for First Order

Rukiye Öztürk Mert(HITIT UNIVERSITY)0000-0001-8083-5304
Sayfa
356–362
Yayın Tarihi
2023-11-30
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Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Son olarak, bu genişlemelerin spektrum yapısı araştırılmıştır.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Bu çalışmada, sonlu simetrik aralıktaki vektör fonksiyonların Hilbert uzayında, birinci mertebeden lineer diferansiyel-operatör ifadesi tarafından doğrulan minimal ve maksimal operatörleri oluşturulmuştur.
📊
Temel Bulgular & Veri:Daha sonra, bu minimal operatörün defekt sayıları hesaplanmış ve sınır değer uzayı oluşturulmuştur.
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Sonuç & Katkı:Son olarak, bu genişlemelerin spektrum yapısı araştırılmıştır.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Normal Diferansiyel Operatör · Defekt Sayıları · Sınır Değer Uzayı

Özet

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.

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.

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Bu Makaleye Atıf Yap

Mert, R. Ö. (2023). Birinci Mertebeden Normal Diferansiyel Operatörlerin Bazı Sınıfları. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, Cilt: 10 Sayı: 2, 356–362. https://doi.org/10.35193/bseufbd.1223029

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