Defining Hausdorff operators on Euclidean spaces
Alexey Karapetyants, Elijah Liflyand
Abstract
After 2000, an interest in the Hausdorff operators grew, first of all in the sense of a diversity of spaces on which these operators were considered. We try to introduce a ‘correct’ definition of the Hausdorff operator on Euclidean spaces. This is supplemented by a variety of known and possible applications.
Topics & Concepts
MathematicsHausdorff spaceUrysohn and completely Hausdorff spacesEuclidean geometryHausdorff distanceOperator (biology)Pure mathematicsVariety (cybernetics)Algebra over a fieldHausdorff measureHausdorff dimensionMathematical analysisGeometryBiochemistryChemistryTranscription factorRepressorGeneStatisticsAdvanced Harmonic Analysis ResearchAdvanced Banach Space TheoryApproximation Theory and Sequence Spaces