Geodesic
Spectral Analysis of Differential Operator with Involution
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 4, pp. 64-78

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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
Mots-clés : spectral decomposition, equiconvergence of spectral decomposition. 
@article{VNGU_2014_14_4_a6,
     author = {E. Yu. Romanova},
     title = {Spectral {Analysis} of {Differential} {Operator} with {Involution}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {64--78},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2014_14_4_a6/}
}
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E. Yu. Romanova. Spectral Analysis of Differential Operator with Involution. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 14 (2014) no. 4, pp. 64-78. http://geodesic.mathdoc.fr/item/VNGU_2014_14_4_a6/