equibounded
Adjective
Having the property that there exists a positive number M such that for all functions f in the family of functions F defined on X, |f(x)| ≤ M for all x in X.
Usage- not-comparable
- of a family of functions
- Examples
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The stability is shown to be uniform with respect to the singular parameter or the solutions are shown to be equibounded.
More examples (1)
An important example of such a semigroup in infinite dimensional Hilbert space is the weak operator closed monothetic semigroup generated by a linear operator with equibounded iterates.