Kernel aggregation operators and their marginals

Binary kernel aggregation operators, that is, monotone binary operators on [0,1] with the Chebyshev norm equal to 1 are studied. Marginal functions of such operators are shown to be 1-Lipschitz. Several constructions of kernel aggregation operators with fixed marginal functions are given, including maximal and minimal kernel aggregation operators with prescribed marginals. Finally, kernel aggregation operators uniquely determined by their marginals are characterized.