<div class="csl-bib-body">
<div class="csl-entry">Knörr, J. (2024, December 17). <i>A Paley-Wiener-Schwartz Theorem for valuations on convex functions</i> [Conference Presentation]. Oberwolfach Workshop on Convex geometry and its applications (ID 2451), Oberwolfach, Germany. http://hdl.handle.net/20.500.12708/223162</div>
</div>
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/223162
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dc.description.abstract
Much of the immense progress in Geometric Valuation Theory over the last 30 years is based on Alesker's solution to McMullen's Conjecture, which characterizes continuous translation invariant valuations on convex bodies as uniform limits of linear combinations of mixed volumes. In fact, Alesker established a much stronger result, called the Irreducibility Theorem, which provides a representation theoretic description of the space of these valuations. One of key consequences of this description was the introduction of the notion of smooth valuations, which enjoy very strong regularity properties and admit a variety of integral and differential geometric descriptions.
In this talk I will present work in progress on a corresponding description of the space of all continuous and dually epi-translation invariant valuations on convex functions, which does not require the representation theoretic machinery used by Alesker. Instead, the main idea is to directly obtain suitable integral representations of these functionals by using a Paley-Wiener-Schwartz-type regularity characterization of certain distributions associated to these valuations in terms of the decaying properties of their Fourier-Laplace transform.
As a consequence, we obtain a description of these valuations as uniform limits of valuations constructed from mixed Monge-Amp\`ere operators, mirroring McMullen's Conjecture.
en
dc.language.iso
en
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dc.subject
valuation on functions
en
dc.subject
distribution
en
dc.subject
Fourier analysis
en
dc.subject
Monge-Ampère operator
en
dc.title
A Paley-Wiener-Schwartz Theorem for valuations on convex functions
en
dc.type
Presentation
en
dc.type
Vortrag
de
dc.type.category
Conference Presentation
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tuw.publication.invited
invited
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tuw.researchTopic.id
C4
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
100
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tuw.publication.orgunit
E104-07 - Forschungsbereich Geometrische Analysis
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tuw.event.name
Oberwolfach Workshop on Convex geometry and its applications (ID 2451)
en
tuw.event.startdate
16-12-2024
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tuw.event.enddate
20-12-2024
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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
Oberwolfach
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tuw.event.country
DE
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tuw.event.institution
Mathematisches Forschungsinstitut Oberwolfach
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tuw.event.presenter
Knörr, Jonas
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tuw.event.track
Single Track
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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.openairetype
conference paper not in proceedings
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item.openairecristype
http://purl.org/coar/resource_type/c_18cp
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item.cerifentitytype
Publications
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item.languageiso639-1
en
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item.grantfulltext
none
-
item.fulltext
no Fulltext
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crisitem.author.dept
E104-07 - Forschungsbereich Geometrische Analysis
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crisitem.author.parentorg
E104 - Institut für Diskrete Mathematik und Geometrie
