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Essential spectrum of non-self-adjoint singular matrix differential operators.
- Source :
-
Journal of Mathematical Analysis & Applications . Jul2017, Vol. 451 Issue 1, p473-496. 24p. - Publication Year :
- 2017
-
Abstract
- The purpose of this paper is to study the essential spectrum of non-self-adjoint singular matrix differential operators in the Hilbert space L 2 ( R ) ⊕ L 2 ( R ) induced by matrix differential expressions of the form (0.1) ( τ 11 ( ⋅ , D ) τ 12 ( ⋅ , D ) τ 21 ( ⋅ , D ) τ 22 ( ⋅ , D ) ) , where τ 11 , τ 12 , τ 21 , τ 22 are respectively m -th, n -th, k -th and 0 order ordinary differential expressions with m = n + k being even. Under suitable assumptions on their coefficients, we establish an analytic description of the essential spectrum. It turns out that the points of the essential spectrum either have a local origin, which can be traced to points where the ellipticity in the sense of Douglis and Nirenberg breaks down, or they are caused by singularity at infinity. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 451
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 121540238
- Full Text :
- https://doi.org/10.1016/j.jmaa.2017.02.017