Schwarz function

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 $\Gamma$ in the complex plane, the Schwarz function $S$ is a uniquely determined analytic function on a neighborhood of $\Gamma$ with the property that $S(z)=z^{*}$ for every point $z\in \Gamma$ .[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.
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.

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[Davis-1] 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.

[Shapiro-2] 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.