Geodesic
Modeling of a Singularly Perturbed Spectral Problem by Means of Self-Adjoint Extensions of the Operators of the Limit
Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 1, pp. 31-48

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We use self-adjoint extensions of differential and integral operators to construct an asymptotic model of the Steklov spectral problem describing surface waves over a bank. Estimates of the modeling error are established, and the following unexpected fact is revealed: an appropriate self-adjoint extension of the operators of the limit problems provides an approximation to the eigenvalues not only in the low- and midfrequency ranges of the spectrum but also on part of the high-frequency range.
Keywords: self-adjoint extension, asymptotics of the spectrum, Steklov spectral problem, surface waves. 
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     author = {S. A. Nazarov},
     title = {Modeling of a {Singularly} {Perturbed} {Spectral} {Problem} by {Means} of {Self-Adjoint} {Extensions} of the {Operators} of the {Limit}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {31--48},
     publisher = {mathdoc},
     volume = {49},
     number = {1},
     year = {2015},
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     url = {http://geodesic.mathdoc.fr/item/FAA_2015_49_1_a2/}
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S. A. Nazarov. Modeling of a Singularly Perturbed Spectral Problem by Means of Self-Adjoint Extensions of the Operators of the Limit. Funkcionalʹnyj analiz i ego priloženiâ, Tome 49 (2015) no. 1, pp. 31-48. http://geodesic.mathdoc.fr/item/FAA_2015_49_1_a2/