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Friedrichs extensions for Sturm–Liouville operators with complex coefficients and their spectra

Part of: Operator theory: Ordinary differential operators Boundary value problems

Published online by Cambridge University Press:  18 November 2022

Zhaowen Zheng ,
Jiangang Qi  and
Jing Shao
Zhaowen Zheng
Affiliation:
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, People's Republic of China (zhwzheng@126.com) College of Mathematics and Systems Science, Guangdong Polytechnic Normal University, Guangzhou 510665, People's Republic of China
Jiangang Qi
Affiliation:
Department of Mathematics, Shandong University at Weihai, Weihai 264209, People's Republic of China (qjg816@163.com)
Jing Shao
Affiliation:
Department of Mathematics, Jining University, Qufu 273155, People's Republic of China (shaojing99500@163.com)
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Abstract

In this paper, we study the Friedrichs extensions of Sturm–Liouville operators with complex coefficients according to the classification of B. M. Brown et al. [3]. We characterize the Friedrichs extensions both by boundary conditions at regular endpoint and asymptotic behaviours of elements in the maximal operator domains at singular endpoint. Some of spectral properties are also involved.

Keywords

Friedrichs extensionSturm–Liouville operatorcomplex coefficientsesquilinear formspectrum

MSC classification

Primary: 47E05: Ordinary differential operators (should also be assigned at least one other classification number in section 47) 34B20: Weyl theory and its generalizations 34B24: Sturm-Liouville theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 6 , December 2023 , pp. 1883 - 1905
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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