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
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.
.
Supporting Institution
Lorestan University
References
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P.37-76,(Russian) (English transl. in Pros.Steklov. Inst. Math. 1987, N1 (170)
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sem.Ptrosk.V.10.1984.P.78-106, Russian, (English transl. In Soviet Math.V.35, N.5, 1986)
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- [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.
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(165) 1984, No. 3, pp. 317-347; English transl. in Math. USSR-sb. 51, 1985.
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148-150(1973)
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262-265 (1972)
Year 2020,
Volume: 4 Issue: 4, 316 - 320, 30.12.2020
Reza Alizadeh
,
Ali Sameripour
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)