Main Article Content
The LULU-Semigroup for Envelopes of Functions
Abstract
In the theory of non-linear smoot
hers a semigroup of operators has been established, that structures the rank
based selectors in a
lattice for the purpose of comparison and analysis. The well known upper and
lower
envelopes of functions can be associated with a pair of operators L and U that
allow a similar structure to be defined. The monoid of
operators that are compositions of these is established, and the
inequalities needed for partially ordering are proved. Some interpretations,
analogies and uses are discussed.
Mathematics Subject Classification (2000): 47H19.
Key words: Non-linear smoothers, semi group of operators, envelopes of functions.
Quaestiones Mathematicae 27 (2004), 89-97.
hers a semigroup of operators has been established, that structures the rank
based selectors in a
lattice for the purpose of comparison and analysis. The well known upper and
lower
envelopes of functions can be associated with a pair of operators L and U that
allow a similar structure to be defined. The monoid of
operators that are compositions of these is established, and the
inequalities needed for partially ordering are proved. Some interpretations,
analogies and uses are discussed.
Mathematics Subject Classification (2000): 47H19.
Key words: Non-linear smoothers, semi group of operators, envelopes of functions.
Quaestiones Mathematicae 27 (2004), 89-97.
