Approximation to the identity
Encyclopedia
In mathematics
, an approximation to the identity refers to a sequence or net that converges to the identity in some algebra. Specifically, it can mean:
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, an approximation to the identity refers to a sequence or net that converges to the identity in some algebra. Specifically, it can mean:
- Nascent delta function, most commonly
- MollifierMollifierIn mathematics, mollifiers are smooth functions with special properties, used in distribution theory to create sequences of smooth functions approximating nonsmooth functions, via convolution...
, more narrowly - Approximate identityApproximate identityIn functional analysis and ring theory, an approximate identity is a net in a Banach algebra or ring that acts as a substitute for an identity element....
, more abstractly