Special Issue in honor of John W. Neuberger. Electron. J. Diff. Eqns., Special Issue 02 (2022), pp. 41-66.

Spectral theory of C-symmetric non-selfadjoint differential operators of order 2n

Horst Behncke, Don Hinton

Abstract:
We continue the spectral analysis of differential operators with complex coefficients, extending some results for Sturm-Liouville operators to higher order operators. We give conditions for the essential spectrum to be empty, and for the operator to have compact resolvent. Conditions are given on the coefficients for the resolvent to be Hilbert-Schmidt. These conditions are new even for real coefficients, i.e., the selfadjoint case. Asymptotic analysis is a central tool.

Published March 27, 2023.
Math Subject Classifications: 34L05, 34B20, 34B27, 34B40, 34B60.
Key Words: m-functions; singular operators; essential spectrum; non-selfadjoint operators; C-symmetric operators; Green's function; asymptotic solutions.
DOI: https://doi.org/10.58997/ejde.sp.02.b2

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Horst Behncke
Fachbereich Mathematik/Informatik
Universitat Osnabruck
49069 Osnabruck, Germany
email: sabine.schroeder@uni-osnabrueck.de
Don Hinton
Mathematics Department
University of Tennessee
Knoxville, TN 37996, USA
email: dhinton1@tennessee.edu

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