KnowraIdentity theoremLinked fromLinked fromThe 20 pages that link to Identity theorem, each with the reason it gives.All 20Related 19Compared with 1Holomorphic functionRelated: It captures how local agreement determines a holomorphic function across its domain.Analytic continuationRelated: It guarantees uniqueness when two proposed extensions overlap.Cauchy's integral formulaRelated: The formula’s analytic consequences help make values on a small set determine a whole function.Maximum modulus principleRelated: Once constancy holds near an interior maximum, this theorem extends it across the connected domain.Meromorphic functionRelated: It also constrains meromorphic functions because their holomorphic regions obey the same uniqueness principle.Entire functionRelated: An entire function is fixed globally by its values on any suitable set.Liouville's theoremRelated: It is another holomorphic rigidity result, but its constraint comes from matching values rather than boundedness.Schwarz lemmaRelated: It explains why matching an equality case at a point can force global agreement.Complex differentiabilityRelated: Regional complex differentiability makes values on a small set determine the entire function.Cauchy estimatesRelated: Derivative control supports the local power-series structure behind this uniqueness result.Removable singularityRelated: An extension across one point remains constrained by the function's values nearby.Weierstrass factorization theoremRelated: It helps explain why zero data can strongly constrain an analytic function.Complex derivativeRelated: Complex differentiability helps make values on a small set determine an entire function.Hurwitz's theoremRelated: It underlies the rigidity behind the theorem's identically-zero alternative.Hartogs extension theoremRelated: Uniqueness ensures that any extension across the hole is determined by the original function.Schwarz reflection principleRelated: Uniqueness of the extension follows from agreement on the original domain.Casorati–Weierstrass theoremRelated: It supports uniqueness arguments that rule out a nonconstant function taking only restricted local values.Analytic functionRelated: Local agreement determines the entire analytic function on a connected domain.Analyticity of holomorphic functionsRelated: Local power-series equality makes agreement on a small set determine the function throughout its domain.Carlson's theoremCompared with: Integer samples have no finite accumulation point, so Carlson needs growth bounds the identity theorem does not.
KnowraIdentity theoremLinked fromLinked fromThe 20 pages that link to Identity theorem, each with the reason it gives.All 20Related 19Compared with 1Holomorphic functionRelated: It captures how local agreement determines a holomorphic function across its domain.Analytic continuationRelated: It guarantees uniqueness when two proposed extensions overlap.Cauchy's integral formulaRelated: The formula’s analytic consequences help make values on a small set determine a whole function.Maximum modulus principleRelated: Once constancy holds near an interior maximum, this theorem extends it across the connected domain.Meromorphic functionRelated: It also constrains meromorphic functions because their holomorphic regions obey the same uniqueness principle.Entire functionRelated: An entire function is fixed globally by its values on any suitable set.Liouville's theoremRelated: It is another holomorphic rigidity result, but its constraint comes from matching values rather than boundedness.Schwarz lemmaRelated: It explains why matching an equality case at a point can force global agreement.Complex differentiabilityRelated: Regional complex differentiability makes values on a small set determine the entire function.Cauchy estimatesRelated: Derivative control supports the local power-series structure behind this uniqueness result.Removable singularityRelated: An extension across one point remains constrained by the function's values nearby.Weierstrass factorization theoremRelated: It helps explain why zero data can strongly constrain an analytic function.Complex derivativeRelated: Complex differentiability helps make values on a small set determine an entire function.Hurwitz's theoremRelated: It underlies the rigidity behind the theorem's identically-zero alternative.Hartogs extension theoremRelated: Uniqueness ensures that any extension across the hole is determined by the original function.Schwarz reflection principleRelated: Uniqueness of the extension follows from agreement on the original domain.Casorati–Weierstrass theoremRelated: It supports uniqueness arguments that rule out a nonconstant function taking only restricted local values.Analytic functionRelated: Local agreement determines the entire analytic function on a connected domain.Analyticity of holomorphic functionsRelated: Local power-series equality makes agreement on a small set determine the function throughout its domain.Carlson's theoremCompared with: Integer samples have no finite accumulation point, so Carlson needs growth bounds the identity theorem does not.