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Hilbert Space FactorizationPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2017 (English)In: Hyponormal Quantization of Planar Domains: Exponential Transform in Dimension Two, Springer, 2017, p. 23-45Chapter in book (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer, 2017. p. 23-45
##### Series

Lecture Notes in Mathematics, ISSN 0075-8434 ; 2199
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-215903DOI: 10.1007/978-3-319-65810-0_3Scopus ID: 2-s2.0-85030700803ISBN: 9783319658094 (print)OAI: oai:DiVA.org:kth-215903DiVA, id: diva2:1149580
#####

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##### Note

The positivity properties of the exponential transform define in a canonical way a Hilbert space ℋ(Ω) and a (co)hyponormal operator acting on it, such that the exponential transform itself appears as a polarized compressed resolvent of this operator. There are many variants of this procedure, but they are all equivalent. Historically the process actually went in the opposite direction starting with an abstract Hilbert space and hyponormal operator with rank one self-commutator, the exponential transform arose as a natural characteristic function obtained as the determinant of the multiplicative commutator of the resolvent. If one considers ℋ(Ω) as a function space, the analytic functions in it are very weak, i.e., have a small norm, and for a special class of domains, the quadrature domains, the analytic subspace, ℋa(Ω), even collapses to a finite dimensional space. Some more general kinds of quadrature domains are discussed in terms of analytic functionals, and we also show that some integral operators based on the exponential transform can be interpreted in terms of Silva-Köthe-Grothendieck duality.

QC 20171016

Available from: 2017-10-16 Created: 2017-10-16 Last updated: 2017-11-29Bibliographically approved
doi
isbn
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