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Zeitschrift für Analysis und ihre Anwendungen


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Volume 8, Issue 3, 1989, pp. 237–260
DOI: 10.4171/ZAA/352

Published online: 1989-06-30

On Spectral Properties of Elliptic Pseudo-Differential Operators Far from Self-Adjoint Ones

M.S. Agranovich and A.S. Markus

We establish a rough asymptotics for eigenvalues of elliptic operators under some assumptions; one of them is that the values of the principal symbol do not cover the whole complex plane. We consider also a collection of some examples of non-self-adjoint elliptic operators: in particular, with unusual formulas for asymptotics of eigenvalues; with a regular asymptotics of eigenvalues but without the completeness of root functions; with a complete system of eigenfunctions which is not a basis.

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Agranovich M.S., Markus A.S. : On Spectral Properties of Elliptic Pseudo-Differential Operators Far from Self-Adjoint Ones. Z. Anal. Anwend. 8 (1989), 237-260. doi: 10.4171/ZAA/352