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On the spectral properties of Non- selfadjoint Elliptic Differential Operators in Hilbert space

Year 2020, Volume: 4 Issue: 4, 316 - 320, 30.12.2020

Reza Alizadeh Ali Sameripour

https://doi.org/10.31197/atnaa.650378

Abstract

The non-self-adjoint operators appear in many branches of science, from kinetic theory and quantum me-
chanics to linearizations of equations of mathematical physics. Non-self-adjoint operators are usually difficult
to study because of the lack of general spectral theory. In this paper, our aim is to study the resolvent and
the spectral properties of a class of non-self-adjoint differential operators.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         



                          .

Keywords

‎resolvent‎ ‎asymptotic spectrum‎ distribution of eigenvalues

Supporting Institution

Lorestan University

References

  • ‎[1] M.S.Agranovich, Elliptic operators on compact manifolds,I.Itogi Nauki I Tekhniki: Sovremennye Problemy Mat :Funda- mental'nye Napravleniya Val.63, VINITI, Moskow.1990, PP.5-129 (Russian)
  • [2] K. Kh. Boimatov and A. G. Kostyuchenko, Distribution of eigenvalues of second-order non-selfadjoint di?erential operators, Vest. Mosk. Gos. Univ., Ser. I, Mat. Mekh, No. 3, 1990, pp. 24-31 (Russian)
  • [3] K. Kh. Boimatov, Asymptotic behaviour of the spectra of second-order non-selfadjoint systems of di?erential operators, Mat. Zametki, Vol. 51, No. 4, 1992, pp. 6-16, (Russian)
  • [4] K. Kh. Boimvatov, Spectral asymptotics of nonselfadjoint degenerate elliptic systems of di?erential operators Dokl. Akad. Nauk. Rossyi, Vol. 330, No.6, 1993,(Russian); (English transl. In Russian Acad.Sci.Dokl. Math. Vol.47, 1993, N3, PP.545- 553)
  • [5] K. Kh. Boimvatov, Separation theorems, weighted spaces and there applications. Trudy Mat. Inst. Steklov. Vol.170,1984, P.37-76,(Russian) (English transl. in Pros.Steklov. Inst. Math. 1987, N1 (170)
  • [6] K. Kh. Boimatov, Spectral asymptotics of di?erential and pseudo-di?erential operators Part.2, Trudy sem.Ptrosk.V.10.1984.P.78-106, Russian, (English transl. In Soviet Math.V.35, N.5, 1986)
  • [7] I. C. Gokhberg and M. G. Krein, Introduction to the Theory of linear non-selfadjoint operators in Hilbert space, English transl. Amer. Math. Soc., Providence, R. I. 1969.
  • [8] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1966.
  • [9] A. Sameripour and K. Seddigh, Distribution of the eigenvalues non-selfadjoint elliptic systems that degenerated on the boundary of domain, (Russian)Mat. Zametki 61(1997), no,3, 463-467 translation in Math. Notes 61(1997) no,3-4. 379-384
  • [10] A. Sameripour, On the Distribution of eigenvalues of degenerate elliptic di?eretial oparetors far from self adjoint ones for general boundary conditions,Ann. Sci.Math.Quebec 27 (2003), no.1,67-89.
  • [11] A. A. Shkalikov, Tauberian type theorems on the distribution of zeros of holomorphic functions, Matem. Sbornik Vol. 123 (165) 1984, No. 3, pp. 317-347; English transl. in Math. USSR-sb. 51, 1985.
  • [12] I.L. Vulis and M. Z. Solomyak, Spectral asymptotics of degenerate elliptic staklov problem, vestn. Leningr. Univ., No:19, 148-150(1973)
  • [13] I.L. Vulis and M. Z. Solomyak, Spectral asymptotics of degenerate elliptic operators, Dokl.Akad. Nauk. SSSR,207,NO.2, 262-265 (1972)

Year 2020, Volume: 4 Issue: 4, 316 - 320, 30.12.2020

Reza Alizadeh Ali Sameripour

https://doi.org/10.31197/atnaa.650378

Abstract

References

  • ‎[1] M.S.Agranovich, Elliptic operators on compact manifolds,I.Itogi Nauki I Tekhniki: Sovremennye Problemy Mat :Funda- mental'nye Napravleniya Val.63, VINITI, Moskow.1990, PP.5-129 (Russian)
  • [2] K. Kh. Boimatov and A. G. Kostyuchenko, Distribution of eigenvalues of second-order non-selfadjoint di?erential operators, Vest. Mosk. Gos. Univ., Ser. I, Mat. Mekh, No. 3, 1990, pp. 24-31 (Russian)
  • [3] K. Kh. Boimatov, Asymptotic behaviour of the spectra of second-order non-selfadjoint systems of di?erential operators, Mat. Zametki, Vol. 51, No. 4, 1992, pp. 6-16, (Russian)
  • [4] K. Kh. Boimvatov, Spectral asymptotics of nonselfadjoint degenerate elliptic systems of di?erential operators Dokl. Akad. Nauk. Rossyi, Vol. 330, No.6, 1993,(Russian); (English transl. In Russian Acad.Sci.Dokl. Math. Vol.47, 1993, N3, PP.545- 553)
  • [5] K. Kh. Boimvatov, Separation theorems, weighted spaces and there applications. Trudy Mat. Inst. Steklov. Vol.170,1984, P.37-76,(Russian) (English transl. in Pros.Steklov. Inst. Math. 1987, N1 (170)
  • [6] K. Kh. Boimatov, Spectral asymptotics of di?erential and pseudo-di?erential operators Part.2, Trudy sem.Ptrosk.V.10.1984.P.78-106, Russian, (English transl. In Soviet Math.V.35, N.5, 1986)
  • [7] I. C. Gokhberg and M. G. Krein, Introduction to the Theory of linear non-selfadjoint operators in Hilbert space, English transl. Amer. Math. Soc., Providence, R. I. 1969.
  • [8] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1966.
  • [9] A. Sameripour and K. Seddigh, Distribution of the eigenvalues non-selfadjoint elliptic systems that degenerated on the boundary of domain, (Russian)Mat. Zametki 61(1997), no,3, 463-467 translation in Math. Notes 61(1997) no,3-4. 379-384
  • [10] A. Sameripour, On the Distribution of eigenvalues of degenerate elliptic di?eretial oparetors far from self adjoint ones for general boundary conditions,Ann. Sci.Math.Quebec 27 (2003), no.1,67-89.
  • [11] A. A. Shkalikov, Tauberian type theorems on the distribution of zeros of holomorphic functions, Matem. Sbornik Vol. 123 (165) 1984, No. 3, pp. 317-347; English transl. in Math. USSR-sb. 51, 1985.
  • [12] I.L. Vulis and M. Z. Solomyak, Spectral asymptotics of degenerate elliptic staklov problem, vestn. Leningr. Univ., No:19, 148-150(1973)
  • [13] I.L. Vulis and M. Z. Solomyak, Spectral asymptotics of degenerate elliptic operators, Dokl.Akad. Nauk. SSSR,207,NO.2, 262-265 (1972)
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Reza Alizadeh 0000-0001-9902-4915

Ali Sameripour This is me

Publication Date December 30, 2020
Published in Issue Year 2020 Volume: 4 Issue: 4

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