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Essential spectra of singular matrix differential operators of mixed order in the limit circle case

✍ Scribed by Jiangang Qi; Shaozhu Chen

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
157 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

The present paper is concerned with the essential spectrum of the singular matrix differential operator of mixed order

over the interval (a, b), where D = d/dt. It is shown that if the coefficients are locally integrable functions and T is in the limit circle case, then the essential spectrum of T is given by the essential range of ${{p(t)d(t)-\vert h(t)\vert^2}\over{p(t)}} $\end{document}. The main idea is to transform the original spectral problem into a spectral problem of a singular Hamiltonian differential operator so that the classical Titchmarsh‐Weyl theory can apply. The approach used here can be applied to many other cases. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim

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## Abstract We consider a system of ordinary differential operators of mixed order on an interval (0, __r__~0~), __r__~0~ > 0, where some of the coefficients are singular at 0. A special case has been dealt with by Kako, where the essential spectrum of an operator associated with a linearized magne