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identity theorem of holomorphic functions

(Theorem)

$\displaystyle f(z) = g(z)$

(1)

is true in an infinite subset

, then (1) is true in the whole

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

"identity theorem of holomorphic functions" is owned by rspuzio. [ full author list (2) | owner history (1) ]

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Other names:

rigidity theorem for analytic functions

This object's parent.

Attachments:: proof of identity theorem of holomorphic functions (Proof) by rspuzio

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Cross-references: arc, neighbourhood, subset, accumulation point, infinite subset, equation, complex plane, domain, holomorphic, functions
There are 5 references to this entry.

This is version 8 of identity theorem of holomorphic functions, born on 2007-03-04, modified 2008-05-01.
Object id is 9016, canonical name is IdentityTheoremOfHolomorphicFunctions.
Accessed 1556 times total.

Classification:

30A99 (Functions of a complex variable :: General properties :: Miscellaneous)

Pending Errata and Addenda

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