Geodesic
Basis Property of Eigen- and Associated Functions of an Operator with Nondense Domain of Definition in the Example of the Orr--Sommerfeld problem
Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 931-937

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In the paper, we propose a method for proving the unconditional basis property of eigen- and associated functions of an integro-differential operator defined on a nondense domain of definition. In particular, we obtain a new simpler proof of the unconditional basis property of eigen- and associated functions of the spectral Orr–Sommerfeld problem, well-known in hydromechanics, which reduces to the eigenvalue problem for the operator under study.
Keywords: Orr–Sommerfeld problem, pencils of differential operators, Riesz basis, unconditional basis
Mots-clés : Sobolev spaces. 
@article{MZM_2017_102_6_a12,
     author = {E. A. Shiryaev},
     title = {Basis {Property} of {Eigen-} and {Associated} {Functions} of an {Operator} with {Nondense} {Domain} of {Definition} in the {Example} of the {Orr--Sommerfeld} problem},
     journal = {Matemati\v{c}eskie zametki},
     pages = {931--937},
     publisher = {mathdoc},
     volume = {102},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a12/}
}
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E. A. Shiryaev. Basis Property of Eigen- and Associated Functions of an Operator with Nondense Domain of Definition in the Example of the Orr--Sommerfeld problem. Matematičeskie zametki, Tome 102 (2017) no. 6, pp. 931-937. http://geodesic.mathdoc.fr/item/MZM_2017_102_6_a12/