Toggle Main Menu Toggle Search

Open Access padlockePrints

The Exponential Transform

Lookup NU author(s): Professor Mihai Putinar


Full text for this publication is not currently held within this repository. Alternative links are provided below where available.


© 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.

Publication metadata

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


DOI: 10.1007/978-3-319-65810-0_2

Library holdings: Search Newcastle University Library for this item

ISBN: 9783319658094