# Line bundles defined by the Schwarz function

Line bundles defined by the Schwarz function Cauchy and exponential transforms are characterized, and constructed, as canonical holomorphic sections of certain line bundles on the Riemann sphere defined in terms of the Schwarz function. A well known natural connection between Schwarz reflection and line bundles defined on the Schottky double of a planar domain is briefly discussed in the same context. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Line bundles defined by the Schwarz function

, Volume 8 (2) – Dec 13, 2017
13 pages

/lp/springer-journals/line-bundles-defined-by-the-schwarz-function-fAebgM5a05
Publisher
Springer Journals
Copyright © 2017 by Springer International Publishing AG, part of Springer Nature
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-017-0201-9
Publisher site
See Article on Publisher Site

### Abstract

Cauchy and exponential transforms are characterized, and constructed, as canonical holomorphic sections of certain line bundles on the Riemann sphere defined in terms of the Schwarz function. A well known natural connection between Schwarz reflection and line bundles defined on the Schottky double of a planar domain is briefly discussed in the same context.

### Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Dec 13, 2017