Korovkin-type theorems for almost periodic measures

Silvia-Otilia Corduneanu¹

¹ Department of Mathematics Gh. Asachi Technical University, Iaşi Bd. Copou 11 6600 Iaşi, Romania

Colloquium Mathematicum, Tome 93 (2002) no. 2, pp. 277-284

Résumé

Some Korovkin-type theorems for spaces containing almost periodic measures are presented. We prove that some sets of almost periodic measures are test sets for some particular nets of positive linear operators on spaces containing almost periodic measures. We consider spaces which contain almost periodic measures defined by densities and measures which can be represented as the convolution between an arbitrary measure with finite support (or an arbitrary bounded measure) and a fixed almost periodic measure. We also give a Korovkin-type result for the space of almost periodic measures; in this case the net of linear operators has a certain contraction property.

Détail

DOI : 10.4064/cm93-2-7

Keywords: korovkin type theorems spaces containing almost periodic measures presented prove sets almost periodic measures test sets particular nets positive linear operators spaces containing almost periodic measures consider spaces which contain almost periodic measures defined densities measures which represented convolution between arbitrary measure finite support arbitrary bounded measure fixed almost periodic measure korovkin type result space almost periodic measures net linear operators has certain contraction property