Araştırma Makalesi
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Multipoint selfadjoint quasi-differential operators for first order

Yıl 2019, Cilt: 68 Sayı: 1, 964 - 972, 01.02.2019
https://doi.org/10.31801/cfsuasmas.501414

Öz

In the present paper, the aim is to described all selfadjoint extensions of the minimal operator generated by first order linear symmetric multipoint quasi-differential operator expression in the direct sum of weighted Hilbert spaces of vector-functions defined at the semi-infinite intervals by using the Calkin-Gorbachuk method. We have also examine the structure of the spectrum of such extensions.

Kaynakça

  • Bairamov E., Öztürk Mert, R, Ismailov, Z., Selfadjoint Extensions of a Singular Differential Operator, Journal of Mathematical Chemistry, 50: (2012), 1100-1110.
  • El-Gebeily, M.A., O'Regan, D., Agarwal, R., Characterization of Self-adjoint Ordinary Differential Operators, Mathematical and Computer Modelling, 54 (2011), 659-672.
  • Everitt, WN, Markus L., The Glazman-Krein-Naimark Theorem for Ordinary Differential Operators, Operator Theory, Advances and Applications, 98 (1997), 118-130.
  • Everitt, W.N., Poulkou A., Some Observations and Remarks on Differential Operators Generated by First-Order Boundary Value Problems, Journal of Computational and Applied Mathematics, 153 (2003), 201-211.
  • Glazman, IM., On the Theory of Singular Differential Operators, Uspehi Math. Nauk., 40 (1950), 102-135 (English translation in Amer. Math. Soc. Translations 1962; (1), 4: 331-372).
  • Gorbachuk, VI, Gorbachuk, ML., Boundary Value Problems for Operator-Differential Equations, First ed., Kluwer Academic Publisher: Dordrecht, 1991.
  • Hörmander, L., On the Theory of General Partial Differential Operators, Acta Mathematica, 94 (1955), 161-248.
  • Naimark, MA., Linear Differential Operators II. Ungar, New York, 1968.
  • von Neumann, J., Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren, Math. Ann. 102 (1929-1930), 49-131.
  • Rofe-Beketov, FS, Kholkin, AM., Spectral Analysis of Differential Operators, World Scientific Monograph Series in Mathematics v.7. 2005.
  • Stone, MH., Linear Transformations in Hilbert Spaces and Their Applications in Analysis, American Math. Soc. Coloq., (1932), 15.
  • Zettl, A, Sun, J., Survey Article: Self-adjoint Ordinary Differential Operators and Their Spectrum, Rocky Mountain Journal of Mathematics, 45, 1 (2015), 763-886.
Yıl 2019, Cilt: 68 Sayı: 1, 964 - 972, 01.02.2019
https://doi.org/10.31801/cfsuasmas.501414

Öz

Kaynakça

  • Bairamov E., Öztürk Mert, R, Ismailov, Z., Selfadjoint Extensions of a Singular Differential Operator, Journal of Mathematical Chemistry, 50: (2012), 1100-1110.
  • El-Gebeily, M.A., O'Regan, D., Agarwal, R., Characterization of Self-adjoint Ordinary Differential Operators, Mathematical and Computer Modelling, 54 (2011), 659-672.
  • Everitt, WN, Markus L., The Glazman-Krein-Naimark Theorem for Ordinary Differential Operators, Operator Theory, Advances and Applications, 98 (1997), 118-130.
  • Everitt, W.N., Poulkou A., Some Observations and Remarks on Differential Operators Generated by First-Order Boundary Value Problems, Journal of Computational and Applied Mathematics, 153 (2003), 201-211.
  • Glazman, IM., On the Theory of Singular Differential Operators, Uspehi Math. Nauk., 40 (1950), 102-135 (English translation in Amer. Math. Soc. Translations 1962; (1), 4: 331-372).
  • Gorbachuk, VI, Gorbachuk, ML., Boundary Value Problems for Operator-Differential Equations, First ed., Kluwer Academic Publisher: Dordrecht, 1991.
  • Hörmander, L., On the Theory of General Partial Differential Operators, Acta Mathematica, 94 (1955), 161-248.
  • Naimark, MA., Linear Differential Operators II. Ungar, New York, 1968.
  • von Neumann, J., Allgemeine Eigenwerttheorie Hermitescher Funktionaloperatoren, Math. Ann. 102 (1929-1930), 49-131.
  • Rofe-Beketov, FS, Kholkin, AM., Spectral Analysis of Differential Operators, World Scientific Monograph Series in Mathematics v.7. 2005.
  • Stone, MH., Linear Transformations in Hilbert Spaces and Their Applications in Analysis, American Math. Soc. Coloq., (1932), 15.
  • Zettl, A, Sun, J., Survey Article: Self-adjoint Ordinary Differential Operators and Their Spectrum, Rocky Mountain Journal of Mathematics, 45, 1 (2015), 763-886.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Makaleler
Yazarlar

Rukiye Öztürk Mert Bu kişi benim 0000-0001-8083-5304

Bülent Yılmaz 0000-0002-1394-230X

Zameddin İ. Ismailov 0000-0001-5193-5349

Yayımlanma Tarihi 1 Şubat 2019
Gönderilme Tarihi 22 Kasım 2017
Kabul Tarihi 1 Haziran 2018
Yayımlandığı Sayı Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

APA Öztürk Mert, R., Yılmaz, B., & Ismailov, Z. İ. (2019). Multipoint selfadjoint quasi-differential operators for first order. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 964-972. https://doi.org/10.31801/cfsuasmas.501414
AMA Öztürk Mert R, Yılmaz B, Ismailov Zİ. Multipoint selfadjoint quasi-differential operators for first order. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2019;68(1):964-972. doi:10.31801/cfsuasmas.501414
Chicago Öztürk Mert, Rukiye, Bülent Yılmaz, ve Zameddin İ. Ismailov. “Multipoint Selfadjoint Quasi-Differential Operators for First Order”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 964-72. https://doi.org/10.31801/cfsuasmas.501414.
EndNote Öztürk Mert R, Yılmaz B, Ismailov Zİ (01 Şubat 2019) Multipoint selfadjoint quasi-differential operators for first order. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 964–972.
IEEE R. Öztürk Mert, B. Yılmaz, ve Z. İ. Ismailov, “Multipoint selfadjoint quasi-differential operators for first order”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 964–972, 2019, doi: 10.31801/cfsuasmas.501414.
ISNAD Öztürk Mert, Rukiye vd. “Multipoint Selfadjoint Quasi-Differential Operators for First Order”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (Şubat 2019), 964-972. https://doi.org/10.31801/cfsuasmas.501414.
JAMA Öztürk Mert R, Yılmaz B, Ismailov Zİ. Multipoint selfadjoint quasi-differential operators for first order. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:964–972.
MLA Öztürk Mert, Rukiye vd. “Multipoint Selfadjoint Quasi-Differential Operators for First Order”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 964-72, doi:10.31801/cfsuasmas.501414.
Vancouver Öztürk Mert R, Yılmaz B, Ismailov Zİ. Multipoint selfadjoint quasi-differential operators for first order. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):964-72.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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