Favard Operators

In functional analysis, a branch of mathematics, the Favard operators are defined by:

: mathcal_n(f)x) = \frac \sum_^\infty

where $x\in\mathbb$, $n\in\mathbb$. They are named after Jean Favard.

Generalizations

A common generalization is:
: mathcal_n(f)x) = \frac \sum_^\infty

where $(\gamma_n)_^\infty$ is a positive sequence that converges to 0. This reduces to the classical Favard operators when $\gamma_n^2=1/(2n)$.

References

* This paper also discussed Szász–Mirakyan operators, which is why Favard is sometimes credited with their development (e.g. Favard–Szász operators

Footnotes

Approximation theory

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