identity theorem of holomorphic functions

If the functions f and g are holomorphic in a domain D of the complex plane and the equation

f(z)=g(z) (1)

is true in an infinite subset S of D having an accumulation pointMathworldPlanetmathPlanetmath z0 in D, then (1) is true in the whole D.

Remark.  The subset S may be e.g. some neighbourhood of z0 or some arc containing z0.

Title identity theorem of holomorphic functions
Canonical name IdentityTheoremOfHolomorphicFunctions
Date of creation 2013-03-22 16:47:05
Last modified on 2013-03-22 16:47:05
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 11
Author rspuzio (6075)
Entry type Theorem
Classification msc 30A99
Synonym rigidity theorem for analytic functions
Related topic IdentityTheoremOfPowerSeries
Related topic IdentityTheorem