Spectral Isoperimetric Inequality for the δ′-Interaction on a Contour

Lotoreichik, Vladimir

doi:10.1007/978-3-030-60453-0_10

Cited by 3 publications

(2 citation statements)

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“…Proof. We again decompose R 2 \ Γ θ in Ω ± as in (14), and for u ∈ L 2 (R 2 ) denote u ± := u| Ω ± , then the expression for the sesquilinear form h θ can be rewritten as…”

Section: Proof By Corollary 16 We Have λmentioning

confidence: 99%

“…They are also of interest from the point of view of the spectral geometry, as one deals with various links between the geometric properties of the potential support and the eigenvalues of the associated differential operators, see e.g. [4,14]. In the present paper we prove some results on the spectral analysis for Schrödinger operators with δ -potentials supported by star graphs in two dimensions (in this precise case, the star graph geometry is completely determined by the angles between the branches).…”

Section: Introductionmentioning

confidence: 99%

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On Schrödinger operators with δ′-potentials supported on star graphs

Pankrashkin

Vogel

2022

J. Phys. A: Math. Theor.

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The spectral properties of two-dimensional Schrödinger operators with δ'-potentials supported on star graphs are discussed. We describe the essential spectrum and give a complete description of situations in which the discrete spectrum is non-trivial but finite. A more detailed study is presented for the case of a star graph with two branches, in particular, the small angle asymptotics for the eigenvalues is obtained.

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“…Proof. We again decompose R 2 \ Γ θ in Ω ± as in (14), and for u ∈ L 2 (R 2 ) denote u ± := u| Ω ± , then the expression for the sesquilinear form h θ can be rewritten as…”

Section: Proof By Corollary 16 We Have λmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%