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Year 2018, Volume: 10, 67 - 73, 29.12.2018

Rukiye Öztürk Mert Pembe İpek Al Bülent Yılmaz Zameddin İ. İsmailov

Abstract

References

  • Coddington, E.A., Extension theory of formally normal and symmetric subspaces, Mem. Amer. Math. Soc., 134 (1973), 1-80.
  • Davis, R. H, Singular Normal Di_erential Operators, Tech. Rep., Dep. Math., California Univ., 1955.
  • Dunford, N., Schwartz, J. T., Linear Operators I, II, Second ed., Interscience, New York, 1958; 1963.
  • Gohberg, I.C., Krein, M.G., Introduction to the Theory of Linear Non-Self-Adjoint Operators, Amer. Math. Soc., Providence, RI, 1969.
  • Gorbachuk, M.L., Self-Adjoint Boundary Value Problems for the Di_erential Equations for Second Order with the Unbounded Operator Coefient, Funktsional. Anal. i Prilozhen. 5 (1971), 10-21 (in Russian).
  • Gorbachuk, V.I., Gorbachuk, M.L., Boundary Value Problems for Operator Di_erential Equations, Kluwer Academic, Dordrecht, 1991.
  • Hörmander, L., On the theory of general partial di_erential operators, Acta Mathematica, 94 (1955), 161-248.
  • Ipek Al, P., Yılmaz, B., Ismailov, Z.I., The general form of normal quasi-di_erential operators for first order and their spectrum, Turkish Journal of Mathematics and Computer Science, 8 (2018), 22-28.
  • Ismailov, Z. I., Compact inverses of first-order normal differential operators, J. Math., Anal. Appl. USA, 320,1(2006),266-278.
  • Kilpi, Y., Über lineare normale transformationen in Hilbertschen raum, Ann. Acad. Sci. Fenn. Math. Ser. AI 154 (1953).
  • Kilpi, Y., Ü ber die anzahl der hypermaximalen normalen fort setzungen normalen transformationen, Ann. Univ. Turkuensis. Ser. AI 65 (1963).
  • Kolmogorov, A.N., Fomin, S.V., Elements of the Theory of Functions and Functional Analysis, Dover Books on Mathematics, 1999.
  • Zettl, A., Sun, J., Survey article: Self-adjoint ordinary differential operators and their spectrum, Roky Mountain Journal of Mathematics, 45,1, (2015), 763-886.

Discreteness of Spectrum of Normal Differential Operators for First Order

Year 2018, Volume: 10, 67 - 73, 29.12.2018

Rukiye Öztürk Mert Pembe İpek Al Bülent Yılmaz Zameddin İ. İsmailov

Abstract

In this work, we investigate the discreteness of spectrum of normal extensions in detail. Later on, the asymptotical behavior of eigenvalues of any normal extension has been examined.

Keywords

Differential operator Formally normal and normal operator Spectrum

References

  • Coddington, E.A., Extension theory of formally normal and symmetric subspaces, Mem. Amer. Math. Soc., 134 (1973), 1-80.
  • Davis, R. H, Singular Normal Di_erential Operators, Tech. Rep., Dep. Math., California Univ., 1955.
  • Dunford, N., Schwartz, J. T., Linear Operators I, II, Second ed., Interscience, New York, 1958; 1963.
  • Gohberg, I.C., Krein, M.G., Introduction to the Theory of Linear Non-Self-Adjoint Operators, Amer. Math. Soc., Providence, RI, 1969.
  • Gorbachuk, M.L., Self-Adjoint Boundary Value Problems for the Di_erential Equations for Second Order with the Unbounded Operator Coefient, Funktsional. Anal. i Prilozhen. 5 (1971), 10-21 (in Russian).
  • Gorbachuk, V.I., Gorbachuk, M.L., Boundary Value Problems for Operator Di_erential Equations, Kluwer Academic, Dordrecht, 1991.
  • Hörmander, L., On the theory of general partial di_erential operators, Acta Mathematica, 94 (1955), 161-248.
  • Ipek Al, P., Yılmaz, B., Ismailov, Z.I., The general form of normal quasi-di_erential operators for first order and their spectrum, Turkish Journal of Mathematics and Computer Science, 8 (2018), 22-28.
  • Ismailov, Z. I., Compact inverses of first-order normal differential operators, J. Math., Anal. Appl. USA, 320,1(2006),266-278.
  • Kilpi, Y., Über lineare normale transformationen in Hilbertschen raum, Ann. Acad. Sci. Fenn. Math. Ser. AI 154 (1953).
  • Kilpi, Y., Ü ber die anzahl der hypermaximalen normalen fort setzungen normalen transformationen, Ann. Univ. Turkuensis. Ser. AI 65 (1963).
  • Kolmogorov, A.N., Fomin, S.V., Elements of the Theory of Functions and Functional Analysis, Dover Books on Mathematics, 1999.
  • Zettl, A., Sun, J., Survey article: Self-adjoint ordinary differential operators and their spectrum, Roky Mountain Journal of Mathematics, 45,1, (2015), 763-886.
There are 13 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Rukiye Öztürk Mert 0000-0001-8083-5304

Pembe İpek Al

Bülent Yılmaz

Zameddin İ. İsmailov

Publication Date December 29, 2018
Published in Issue Year 2018 Volume: 10

Cite

APA Öztürk Mert, R., İpek Al, P., Yılmaz, B., İ. İsmailov, Z. (2018). Discreteness of Spectrum of Normal Differential Operators for First Order. Turkish Journal of Mathematics and Computer Science, 10, 67-73.
AMA Öztürk Mert R, İpek Al P, Yılmaz B, İ. İsmailov Z. Discreteness of Spectrum of Normal Differential Operators for First Order. TJMCS. December 2018;10:67-73.
Chicago Öztürk Mert, Rukiye, Pembe İpek Al, Bülent Yılmaz, and Zameddin İ. İsmailov. “Discreteness of Spectrum of Normal Differential Operators for First Order”. Turkish Journal of Mathematics and Computer Science 10, December (December 2018): 67-73.
EndNote Öztürk Mert R, İpek Al P, Yılmaz B, İ. İsmailov Z (December 1, 2018) Discreteness of Spectrum of Normal Differential Operators for First Order. Turkish Journal of Mathematics and Computer Science 10 67–73.
IEEE R. Öztürk Mert, P. İpek Al, B. Yılmaz, and Z. İ. İsmailov, “Discreteness of Spectrum of Normal Differential Operators for First Order”, TJMCS, vol. 10, pp. 67–73, 2018.
ISNAD Öztürk Mert, Rukiye et al. “Discreteness of Spectrum of Normal Differential Operators for First Order”. Turkish Journal of Mathematics and Computer Science 10 (December 2018), 67-73.
JAMA Öztürk Mert R, İpek Al P, Yılmaz B, İ. İsmailov Z. Discreteness of Spectrum of Normal Differential Operators for First Order. TJMCS. 2018;10:67–73.
MLA Öztürk Mert, Rukiye et al. “Discreteness of Spectrum of Normal Differential Operators for First Order”. Turkish Journal of Mathematics and Computer Science, vol. 10, 2018, pp. 67-73.
Vancouver Öztürk Mert R, İpek Al P, Yılmaz B, İ. İsmailov Z. Discreteness of Spectrum of Normal Differential Operators for First Order. TJMCS. 2018;10:67-73.
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