Sharp eigenvalue asymptotics for fourth order operators on the circle

Badanin, Andrey

doi:10.1016/j.jmaa.2014.03.069

Cited by 12 publications

(13 citation statements)

References 19 publications

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“…All eigenvalues λ n , n 1 are zeros of this determinant. Using the sharp asymptotics of the fundamental solutions from [BK4] we determine asymptotics of the determinant (the corresponding proof is rather technical, see Section 7). Analysis of this asymptotics provides the sharp asymptotics of λ n .…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Inverse problems and sharp eigenvalue asymptotics for Euler–Bernoulli operators

Badanin

2015

Inverse Problems

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We consider Euler-Bernoulli operators with real coefficients on the unit interval. We prove the following results: i) Ambarzumyan type theorem about the inverse problems for the Euler-Bernoulli operator.ii) The sharp asymptotics of eigenvalues for the Euler-Bernoulli operator when its coefficients converge to the constant function.iii) The sharp eigenvalue asymptotics both for the Euler-Bernoulli operator and fourth order operators (with complex coefficients) on the unit interval at high energy.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

“…In this section we determine asymptotics of the determinant D(λ). Our proof is based on the sharp asymptotics of the monodromy matrix from our paper [BK4] by using the matrix form of the standard Birkhoff approach. Introduce a diagonal 4 × 4 -matrix ω given by…”

Section: The Barcilon-gottlieb Transformationmentioning

confidence: 99%

Inverse problems and sharp eigenvalue asymptotics for Euler–Bernoulli operators

Badanin

2015

Inverse Problems

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“…Eigenvalue asymptotics for fourth and higher order operators on the finite interval are much less investigated than for second order operators. An operator ∂ 4 + ∂p∂ + q under the 2-periodic boundary conditions was considered by Badanin and Korotyaev [BK2], [BK4] (for the simpler case ∂ 4 + q see [BK1]). The sharp eigenvalue asymptotics for the operator H in the class of complex coefficients was determined in [BK6].…”

Section: Introduction and Main Resultsmentioning

confidence: 99%