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The Exponential Transform
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2017 (English)In: Hyponormal Quantization of Planar Domains: Exponential Transform in Dimension Two, Springer, 2017, p. 7-21Chapter in book (Refereed)
Abstract [en]

The basic definitions of the exponential transform EΩ(z, w) of a planar domain Ω⊂ ℂ and various functions derived from it are recorded in this chapter. The exponential moments having the exponential transform as the generating function are introduced. In addition, several positivity properties of the exponential transform are established. Finally, it is shown that the exponential transform, as a function of z with w kept fixed, can be characterized as being (part of) the unique holomorphic section of a certain line bundle over the Riemann sphere taking a prescribed value at infinity, or alternatively as being the unique solution of a corresponding Riemann-Hilbert problem.

Place, publisher, year, edition, pages
Springer, 2017. p. 7-21
Series
Lecture Notes in Mathematics, ISSN 0075-8434 ; 2199
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-215904DOI: 10.1007/978-3-319-65810-0_2Scopus ID: 2-s2.0-85030682714ISBN: 978-3-319-65809-4 (print)OAI: oai:DiVA.org:kth-215904DiVA, id: diva2:1149814
Note

QC 20171017

Available from: 2017-10-17 Created: 2017-10-17 Last updated: 2017-10-17Bibliographically approved

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