Spectral estimates for dirichlet laplacian on tubes with exploding twisting velocity

Diana Barseghyan; Andrii Khrabustovskyi

doi:10.7153/oam-2019-13-21

Spectral estimates for dirichlet laplacian on tubes with exploding twisting velocity

Diana Barseghyan, Andrii Khrabustovskyi

Institute of Applied Mathematics (5040)

Research output: Contribution to journal › Article › peer-review

Abstract

We study the spectrum of the Dirichlet Laplacian on an unbounded twisted tube with twisting velocity exploding to infinity. If the tube cross section does not intersect the axis of rotation, then its spectrum is purely discrete under some additional conditions on the twisting velocity (D. Krejčiřík, 2015). In the current work we prove a Berezin type upper bound for the eigenvalue moments.

Original language	English
Pages (from-to)	311-322
Number of pages	12
Journal	Operators and Matrices
Volume	13
Issue number	2
DOIs	https://doi.org/10.7153/oam-2019-13-21
Publication status	Published - 1 Jun 2019

Keywords

Dirichlet Laplacian
Discrete spectrum
Eigenvalue bounds
Twisted tube

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.7153/oam-2019-13-21

Cite this

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abstract = "We study the spectrum of the Dirichlet Laplacian on an unbounded twisted tube with twisting velocity exploding to infinity. If the tube cross section does not intersect the axis of rotation, then its spectrum is purely discrete under some additional conditions on the twisting velocity (D. Krej{\v c}i{\v r}{\'i}k, 2015). In the current work we prove a Berezin type upper bound for the eigenvalue moments.",

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KW - Eigenvalue bounds

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Spectral estimates for dirichlet laplacian on tubes with exploding twisting velocity

Abstract

Keywords

ASJC Scopus subject areas

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