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Lookup NU author(s): Professor Mihai Putinar
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© Springer International Publishing AG 2017. 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.
Author(s): Gustafsson B, Putinar M
Editor(s): Gustafsson B; Putinar M
Publication type: Book Chapter
Publication status: Published
Book Title: Hyponormal Quantization of Planar Domains
Year: 2017
Volume: 2199
Pages: 7-21
Print publication date: 18/10/2017
Acceptance date: 02/04/2016
Series Title: Lecture Notes in Mathematics
Publisher: Springer Verlag
Place Published: Cham
URL: https://doi.org/10.1007/978-3-319-65810-0_2
DOI: 10.1007/978-3-319-65810-0_2
Library holdings: Search Newcastle University Library for this item
ISBN: 9783319658094
