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Investigation of the Spectral Properties of a Non-Self-Adjoint Elliptic Differential Operator

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  • Arezoo Ghaedrahmati
  • Ali Sameripour
  • Seppo Hassi

Abstract

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 H1=L2Ω1. Then, as the application of this new result, the resolvent of the considered operator in ℓ-dimensional space Hilbert Hℓ=L2Ωℓ is obtained utilizing some analytic techniques and diagonalizable way.

Suggested Citation

  • Arezoo Ghaedrahmati & Ali Sameripour & Seppo Hassi, 2021. "Investigation of the Spectral Properties of a Non-Self-Adjoint Elliptic Differential Operator," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2021, pages 1-7, May.
    • Handle: RePEc:hin:jijmms:5564552
    DOI: 10.1155/2021/5564552
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