<div class="csl-bib-body">
<div class="csl-entry">Pruckner, R., & Woracek, H. (2022). A growth estimate for the monodromy matrix of a canonical system. <i>Journal of Spectral Theory</i>, <i>12</i>(4), 1623–1657. https://doi.org/10.4171/JST/437</div>
</div>
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dc.identifier.issn
1664-039X
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/187327
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dc.description.abstract
We investigate the spectrum of 2-dimensional canonical systems in the limit circle case. It is discrete and, by the Krein–de Branges formula, cannot be more dense than the integers. But in many cases it will be more sparse. The spectrum of a particular selfadjoint realisation coincides with the zeroes of one entry of the monodromy matrix of the system. Classical function theory thus establishes an immediate connection between the growth of the monodromy matrix and the distribution of the spectrum.
We prove a general and flexible upper estimate for the monodromy matrix, use it to prove a bound for the case of a continuous Hamiltonian, and construct examples which show that this bound is sharp. The first two results run along the lines of earlier work by R. Romanov, but significantly improve upon these results. This is seen even on the rough scale of exponential order.
en
dc.description.sponsorship
FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
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dc.language.iso
en
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dc.publisher
EUROPEAN MATHEMATICAL SOC
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dc.relation.ispartof
Journal of Spectral Theory
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dc.subject
Canonical system
en
dc.subject
asymptotic of eigenvalues
en
dc.subject
order of entire function
en
dc.title
A growth estimate for the monodromy matrix of a canonical system
en
dc.type
Article
en
dc.type
Artikel
de
dc.description.startpage
1623
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dc.description.endpage
1657
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dc.relation.grantno
P 30715-N35
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dc.type.category
Original Research Article
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tuw.container.volume
12
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tuw.container.issue
4
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tuw.journal.peerreviewed
true
-
tuw.peerreviewed
true
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tuw.project.title
Order and type of canonical systems
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tuw.researchTopic.id
C4
-
tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
100
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dcterms.isPartOf.title
Journal of Spectral Theory
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tuw.publication.orgunit
E101-01 - Forschungsbereich Analysis
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tuw.publication.orgunit
E058-02-3 - Fachgruppe Patent- und Lizenzmanagement
-
tuw.publication.orgunit
E101 - Institut für Analysis und Scientific Computing
-
tuw.publication.orgunit
E058-02 - Fachbereich Forschungs- und Transfersupport
-
tuw.publication.orgunit
E058 - Forschungs-, Technologie- und Innovationssupport
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tuw.publisher.doi
10.4171/JST/437
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dc.identifier.eissn
1664-0403
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dc.description.numberOfPages
35
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dc.description.sponsorshipexternal
FWF Fonds zur Förderung der wissenschaftlichen Forschung (FWF)
-
dc.relation.grantnoexternal
Nonlinear Wave Equations and Krein-de Branges theory I4600
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wb.sci
true
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wb.sciencebranch
Mathematik
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wb.sciencebranch.oefos
1010
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wb.sciencebranch.value
100
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item.cerifentitytype
Publications
-
item.openairetype
research article
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item.fulltext
no Fulltext
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item.languageiso639-1
en
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item.openairecristype
http://purl.org/coar/resource_type/c_2df8fbb1
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item.grantfulltext
none
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crisitem.author.dept
E058-02-3 - Fachgruppe Patent- und Lizenzmanagement
-
crisitem.author.dept
E101-01 - Forschungsbereich Analysis
-
crisitem.author.parentorg
E058-02 - Fachbereich Forschungs- und Transfersupport
-
crisitem.author.parentorg
E101 - Institut für Analysis und Scientific Computing