Spectral Properties of a Non-Self-Adjoint Differential Operator with Block-Triangular Operator Coefficients
<p id="p1">In this chapter, the Sturm-Liouville equation with block-triangular, increasing at infinity operator potential is considered. A fundamental system of solutions is constructed, one of which decreases at infinity, and the second increases. The asymptotic behavior at infinity was found out....
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| Main Author: | |
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| Format: | Book Chapter |
| Language: | English |
| Published: |
IntechOpen
2021
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| Subjects: | |
| Online Access: | https://www.intechopen.com/chapters/74945 |
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| Summary: | <p id="p1">In this chapter, the Sturm-Liouville equation with block-triangular, increasing at infinity operator potential is considered. A fundamental system of solutions is constructed, one of which decreases at infinity, and the second increases. The asymptotic behavior at infinity was found out. The Green’s function and the resolvent for a non-self-adjoint differential operator are constructed. This allows to obtain sufficient conditions under which the spectrum of this non-self-adjoint differential operator is real and discrete. For a non-self-adjoint Sturm-Liouville operator with a triangular matrix potential growing at infinity, an example of operator having spectral singularities is constructed.</p> |
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| ISBN: | 978-1-83968-656-6 |
| DOI: | 10.5772/intechopen.95820 |