Investigation of the Spectral Properties of a Non-Self-Adjoint Elliptic Differential Operator
2021 ◽
Vol 2021
◽
pp. 1-7
Keyword(s):
Non-self-adjoint operators have many applications, including quantum and heat equations. On the other hand, the study of these types of operators is more difficult than that of self-adjoint operators. In this paper, our aim is to study the resolvent and the spectral properties of a class of non-self-adjoint differential operators. So we consider a special non-self-adjoint elliptic differential operator (Au)(x) acting on Hilbert space and first investigate the spectral properties of space H 1 = L 2 Ω 1 . Then, as the application of this new result, the resolvent of the considered operator in ℓ -dimensional space Hilbert H ℓ = L 2 Ω ℓ is obtained utilizing some analytic techniques and diagonalizable way.
1978 ◽
Vol 83
(3)
◽
pp. 393-401
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1988 ◽
Vol 44
(3)
◽
pp. 324-349
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1975 ◽
Vol 77
(2)
◽
pp. 337-347
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1979 ◽
Vol 84
(1-2)
◽
pp. 117-134
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1999 ◽
Vol 129
(1)
◽
pp. 165-179
1987 ◽
Vol 29
(1)
◽
pp. 93-97
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Keyword(s):
Keyword(s):