Favard operator
Encyclopedia
In functional analysis
, a branch of mathematics
, the Favard operators are defined by:
where
, 
, and 
. They are named after Jean Favard
.
where
is a positive sequence that converges
to 0. This reduces to the classical Favard operators when
.
Functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure and the linear operators acting upon these spaces and respecting these structures in a suitable sense...
, a branch of mathematics
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...
, the Favard operators are defined by:
where
, , and . They are named after Jean FavardJean Favard
Jean Favard was a French mathematician who worked on analysis.During World War II he was a prisoner of war in Germany.He also was a President of the French Mathematical Society in 1946....
.
Generalizations
A common generalization is:where
is a positive sequence that convergesLimit of a sequence
The limit of a sequence is, intuitively, the unique number or point L such that the terms of the sequence become arbitrarily close to L for "large" values of n...
to 0. This reduces to the classical Favard operators when
.