TRANSMISSION EIGENVALUES FOR MULTIPOINT SCATTERERS

Petr G. Grinevich; Roman G. Novikov

doi:10.32523/2306-6172-2021-9-4-17-25

TRANSMISSION EIGENVALUES FOR MULTIPOINT SCATTERERS

Petr G. Grinevich
, Roman G. Novikov

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

Abstract

We study the transmission eigenvalues for the multipoint scatterers of the Bethe-Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions d = 2 and d = 3. We show that for these scatterers: 1) each positive energy E is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex E is an interior transmission eigenvalue of infinite multiplicity. The case of dimension d = 1 is also discussed.

Original language	English
Pages (from-to)	17-25
Number of pages	9
Journal	Eurasian Journal of Mathematical and Computer Applications
Volume	9
Issue number	4
DOIs	https://doi.org/10.32523/2306-6172-2021-9-4-17-25
Publication status	Published - 1 Jan 2021

Keywords

Multipoint scatterers
Schrödinger equation
Transmission eigenvalues
Transparency

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10.32523/2306-6172-2021-9-4-17-25

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title = "TRANSMISSION EIGENVALUES FOR MULTIPOINT SCATTERERS",

abstract = "We study the transmission eigenvalues for the multipoint scatterers of the Bethe-Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions d = 2 and d = 3. We show that for these scatterers: 1) each positive energy E is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex E is an interior transmission eigenvalue of infinite multiplicity. The case of dimension d = 1 is also discussed.",

keywords = "Multipoint scatterers, Schr{\"o}dinger equation, Transmission eigenvalues, Transparency",

author = "Grinevich, \{Petr G.\} and Novikov, \{Roman G.\}",

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doi = "10.32523/2306-6172-2021-9-4-17-25",

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T1 - TRANSMISSION EIGENVALUES FOR MULTIPOINT SCATTERERS

AU - Grinevich, Petr G.

AU - Novikov, Roman G.

PY - 2021/1/1

Y1 - 2021/1/1

N2 - We study the transmission eigenvalues for the multipoint scatterers of the Bethe-Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions d = 2 and d = 3. We show that for these scatterers: 1) each positive energy E is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex E is an interior transmission eigenvalue of infinite multiplicity. The case of dimension d = 1 is also discussed.

AB - We study the transmission eigenvalues for the multipoint scatterers of the Bethe-Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions d = 2 and d = 3. We show that for these scatterers: 1) each positive energy E is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex E is an interior transmission eigenvalue of infinite multiplicity. The case of dimension d = 1 is also discussed.

KW - Multipoint scatterers

KW - Schrödinger equation

KW - Transmission eigenvalues

KW - Transparency

UR - https://www.scopus.com/pages/publications/85122454421

U2 - 10.32523/2306-6172-2021-9-4-17-25

DO - 10.32523/2306-6172-2021-9-4-17-25

M3 - Article

AN - SCOPUS:85122454421

SN - 2306-6172

VL - 9

SP - 17

EP - 25

JO - Eurasian Journal of Mathematical and Computer Applications

JF - Eurasian Journal of Mathematical and Computer Applications

IS - 4

ER -

TRANSMISSION EIGENVALUES FOR MULTIPOINT SCATTERERS

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