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A field theoretic operator model and Cowen-Douglas class
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-3125-3030
Univ Calif Santa Barbara, Dept Math, Santa Barbara, CA 93106 USA.;Newcastle Univ, Sch Math Stat & Phys, Newcastle Upon Tyne NE1 7RU, Tyne & Wear, England..
2019 (English)In: Banach Journal of Mathematical Analysis, ISSN 1735-8787, Vol. 13, no 2, p. 338-358Article in journal (Refereed) Published
Abstract [en]

In resonance with a recent geometric framework proposed by Douglas and Yang, we develop a functional model for certain linear bounded operators with rank-one self-commutator acting on a Hilbert space. By taking advantage of the refined existing theory of the principal function of a hyponormal operator, we transfer the whole action outside the spectrum, on the resolvent of the underlying operator, localized at a distinguished vector. The whole construction turns out to rely on an elementary algebra body involving analytic multipliers and Cauchy transforms. We propose a natural field theory interpretation of the resulting resolvent functional model.

Place, publisher, year, edition, pages
Duke University Press, 2019. Vol. 13, no 2, p. 338-358
Keywords [en]
hyponormal operator, exponential transform, Cauchy transform, ideal fluid flow
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-249866DOI: 10.1215/17358787-2018-0041ISI: 000462021700005OAI: oai:DiVA.org:kth-249866DiVA, id: diva2:1307252
Note

QC 20190426

Available from: 2019-04-26 Created: 2019-04-26 Last updated: 2019-04-26Bibliographically approved

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Gustafsson, Björn

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