<div class="csl-bib-body">
<div class="csl-entry">Rainer, A. (2024, December 12). <i>On the Regularity of the solution map for polynomials</i> [Presentation]. AKOR Seminar, Wien, Austria.</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/208347
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dc.description.abstract
How do the roots of a monic polynomial whose coefficients depend smoothly on parameters depend on those parameters? This question plays an important role in many areas, e.g., PDEs, perturbation theory of linear operators, and local smooth analysis. The subject, which started with Rellich’s work in the 1930s, enjoyed sustained interest through time that intensified in the last two decades, bringing some definitive optimal results. In particular, if the coefficients are of class $C^{d-1,1}$, where $d$ is the degree of the polynomial, then any continuous root is of Sobolev class $W^{1,q}$, for each $1 \le q < d/(d-1)$. In this talk, I will discuss this optimal result and recent work investigating the continuity of the solution map “coefficients-to-roots”. Joint work with Adam Parusinski
en
dc.language.iso
en
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dc.subject
complex polynomials
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dc.subject
hyperbolic polynomials
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dc.subject
Sobolev regularity of the roots
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dc.subject
continuity of the solution map
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dc.subject
multivalued Sobolev functions
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dc.subject
Wasserstein space
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dc.title
On the Regularity of the solution map for polynomials
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dc.type
Presentation
en
dc.type
Vortrag
de
dc.type.category
Presentation
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tuw.publication.invited
invited
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tuw.researchTopic.id
A3
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tuw.researchTopic.name
Fundamental Mathematics Research
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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tuw.event.name
AKOR Seminar
en
dc.description.sponsorshipexternal
FWF
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dc.relation.grantnoexternal
PAT1381823
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tuw.event.startdate
12-12-2024
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tuw.event.enddate
12-12-2024
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tuw.event.online
On Site
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tuw.event.type
Event for scientific audience
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tuw.event.place
Wien
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tuw.event.country
AT
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tuw.event.institution
VADOR, TU Wien
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tuw.event.presenter
Rainer, Armin
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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.openairecristype
http://purl.org/coar/resource_type/R60J-J5BD
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item.openairetype
conference presentation
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item.cerifentitytype
Publications
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item.fulltext
no Fulltext
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item.languageiso639-1
en
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item.grantfulltext
none
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crisitem.author.dept
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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crisitem.author.parentorg
E105 - Institut für Stochastik und Wirtschaftsmathematik
