The Lu Lu-semigroup for Envelopes Of Functions

In the theory of non-linear smoothers 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...

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Bibliographic Details
Published inQuaestiones mathematicae Vol. 27; no. 1; pp. 89 - 97
Main Authors Malkowsky, E., Rohwer, C.H.
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.03.2004
Subjects
ENVELOPES OF FUNCTIONS
NON-LINEAR SMOOTHERS
SEMIGROUP OF OPERATORS
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Summary:In the theory of non-linear smoothers 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.
ISSN:1607-3606
1727-933X
DOI:10.2989/16073600409486086