The Titchmarsh Convolution Theorem describes the support of the convolution of two functions on the real line, showing that if the convolution vanishes on an interval near a given point, the two original functions must together leave a matching gap near their own combined starting points. Proved by Edward Charles Titchmarsh in 1926, it is a classical uniqueness result of analysis with consequences for integral equations and for questions of when a function can be represented as a Laplace transform.
Facts
StatementDescribes the support of the convolution of two functions: if integrable functions phi and psi have convolution vanishing almost everywhere on 0 < x < kappa, then there exist lambda >= 0 and mu >= 0 with lambda + mu >= kappa such that phi = 0 almost everywhere on (0, lambda) and psi = 0 almost everywhere on (0, mu). 1 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Titchmarsh convolution theorem (Wikipedia)
Introduction, sentence 1
describes the properties of the support of the convolution of two functions
Introduction, sentence 2
It was proven by Edward Charles Titchmarsh in 1926
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