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Abstract
TheSchwarz reflection principle states that given a functionf(z) of a complex variablez such thatf(z) is real in a finite segment\(\Gamma \) of the real axis.
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Notes
- 1.
The notation of Ref. [15] for a infinite definite limit refers to the fact that the function should tend to this infinite limit steadily without oscillating.
- 2.
In the manipulations for the demonstration of this theorem we take that the vanishing limits for\(x\rightarrow \infty \) tend to zero at least as\(x^{-\gamma }\) with\(\gamma >0\).
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Departamento de Física, Universidad de Murcia, Murcia, Spain
José Antonio Oller
- José Antonio Oller
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Correspondence toJosé Antonio Oller.
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Oller, J.A. (2019). Important Mathematical Results: Schwarz Reflection Principle, Sugawara–Kanazawa Theorem, and Herglotz Theorem. In: A Brief Introduction to Dispersion Relations. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-13582-9_4
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