Modeling of a singularly perturbed spectral problem by means of self-adjoint extensions of the operators of the limit problems

Research output

3 Citations (Scopus)

Abstract

© 2015, Springer Science+Business Media New York.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.
Original languageEnglish
Pages (from-to)25-39
JournalFunctional Analysis and its Applications
Issue number1
DOIs
Publication statusPublished - 2015

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Self-adjoint Extension
Singularly Perturbed Problem
Spectral Problem
Surface waves
Modeling Error
Surface Waves
Operator
Modeling
Integral Operator
Range of data
Differential operator
Industry
Eigenvalue
Approximation
Estimate
Model
Business
Banks

Cite this

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title = "Modeling of a singularly perturbed spectral problem by means of self-adjoint extensions of the operators of the limit problems",
abstract = "{\circledC} 2015, Springer Science+Business Media New York.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.",
author = "S.A. Nazarov",
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AB - © 2015, Springer Science+Business Media New York.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.

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