Schwarz function
Appearance
The Schwarz function, named for Hermann Schwarz, was introduced in a 1974 book by Philip J. Davis.[1][2] It defines a method by which the Schwarz reflection principle may be generalized to reflection through arbitrary analytic curves in the complex plane, not just through the real axis. Given a non-singular, analytic Jordan arc in the complex plane, the Schwarz function is a uniquely determined analytic function on a neighborhood of with the property that for every point .[2]: 3
References
- ^ Davis, Philip J. (1974). The Schwarz function and its applications. Carus Monographs 17. Mathematical Association of America. ISBN 978-0-883-85017-6. OCLC 912405492.
- ^ a b Shapiro, Harold S. (1992-03-18). The Schwarz Function and Its Generalization to Higher Dimensions. John Wiley & Sons. ISBN 978-0-471-57127-8. OCLC 924755133.