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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2014, Volume 14, Issue 4, Pages 64–78 (Mi vngu356)  
Spectral Analysis of Differential Operator with Involution

E. Yu. Romanova

Voronezh State University
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Abstract: The paper deals with the differential operator $L$ with involution, defined by a differential expression $l(y)=y'(x) - q(x)y(\omega-x)$ where $q\in L_2[0,\omega]$ and boundary conditions $y(0)=y(\omega).$ The method of similar operators is used to analyze the spectral properties of the operator. The asymptotic of spectrum and the estimations for equiconvergence of spectral decomposition are obtained.
Keywords: spectrum of operator, differential operator with involution, similar operators method, asymptotic of spectrum, spectral decomposition, equiconvergence of spectral decomposition.
Received: 25.12.2013
English version:
Journal of Mathematical Sciences, 2016, Volume 213, Issue 6, Pages 897–909
DOI: https://doi.org/10.1007/s10958-016-2750-0
Document Type: Article
UDC: 517.19
Language: Russian
Citation: E. Yu. Romanova, “Spectral Analysis of Differential Operator with Involution”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 14:4 (2014), 64–78; J. Math. Sci., 213:6 (2016), 897–909
Citation in format AMSBIB
\Bibitem{Rom14}
\by E.~Yu.~Romanova
\paper Spectral Analysis of Differential Operator with Involution
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2014
\vol 14
\issue 4
\pages 64--78
\mathnet{http://mi.mathnet.ru/vngu356}
\transl
\jour J. Math. Sci.
\yr 2016
\vol 213
\issue 6
\pages 897--909
\crossref{https://doi.org/10.1007/s10958-016-2750-0}
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    		Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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