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Date: 23-5-2019
2195
Date: 12-10-2018
1870
Date: 21-8-2018
1587
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Let be analytic on a domain , and assume that never vanishes. Then if there is a point such that for all , then is constant.
Let be a bounded domain, let be a continuous function on the closed set that is analytic on , and assume that never vanishes on . Then the minimum value of on (which always exists) must occur on . In other words,
REFERENCES:
Krantz, S. G. "The Minimum Principle." §5.4.3 in Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 77, 1999.
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