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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2026 / Volume: 69 Issue: 1

First order maximally dissipative singular differential operators

Pembe İpek Al(Karadeniz Technical University)0000-0002-6111-1121
Zameddin Ismaılov(Karadeniz Technical University)0000-0001-5193-5349
Sayfa
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Yayın Tarihi
2020-06-30
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, the results are supported by an application.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, using the Calkin-Gorbachuk method, the general form of all maximal dissipative extensions of the minimal operator generated by first order linear multipoint symmetric singular differential-operator expression in the direct sum of Hilbert space of vector-functions has been found.
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Temel Bulgular & Veri:Later on, the structure of spectrum of these extensions is researched.
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Sonuç & Katkı:Finally, the results are supported by an application.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Dissipative differential operator · selfadjoint differential operator · deficiency index

Abstract

In this paper, using the Calkin-Gorbachuk method, the general form of all maximal dissipative extensions of the minimal operator generated by first order linear multipoint symmetric singular differential-operator expression in the direct sum of Hilbert space of vector-functions has been found. Later on, the structure of spectrum of these extensions is researched. Finally, the results are supported by an application.

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Bu Makaleye Atıf Yap

Al, P. İ., Ismaılov, Z. (2020). First order maximally dissipative singular differential operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 69 Issue: 1. https://doi.org/10.31801/cfsuasmas.643349

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Kaynakça (9)

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  3. Gorbachuk, V. I., Gorbachuk, M. L., Boundary Value Problems for Operator Differential Equations, Dordrecht, the Netherlands, Kluwer Academic Publishers, 1991.
  4. Hörmander, L., On the theory of general partial differential operators, Acta Mathematica, 94 (1955), 161-248.
  5. Ismailov, Z. I., Ipek, P., Selfadjoint singular differential operators of first order and their spectrum, Electronic Journal of Differential Equations, 21 (2016), 1-9.
  6. Nagy, Sz. B., Foias, C., Analyse Harmonique des Operateurs de L' espace de Hilbert, Masson, Paris and Akad Kiodo, Budapest, 1997, English transl. North-Holland, Amesterdam and Akad Kiado, Budapest, 1970.
  7. Naimark, M. A., Linear Differential Operators, New York, USA, Frederick Ungar Publishing Company, 1968.
  8. Rofe-Beketov, F. S., Kholkin, A. M., Spectral Analysis of Differential Operators, USA, World Scientific Monograph Series in Mathematics 7, 2005.
  9. von Neumann, J., Allgemeine eigenwerttheories hermitescher funktionaloperatoren, Mathematische Annalen, 102 (1929-1930), 49-131 (in German).