51. On the Discrepancy Normed Space of Event Sequences for Threshold-based Sampling
- Author
-
Moser, Bernhard A.
- Subjects
Mathematics - Metric Geometry ,Electrical Engineering and Systems Science - Signal Processing ,46Exx, 54C35, 26B39, 26A45, 46B20, 94Axx - Abstract
Recalling recent results on the characterization of threshold-based sampling as quasi-isometric mapping, mathematical implications on the metric and topological structure of the space of event sequences are derived. In this context, the space of event sequences is extended to a normed space equipped with Hermann Weyl's discrepancy measure. Sequences of finite discrepancy norm are characterized by a Jordan decomposition property. Its dual norm turns out to be the norm of total variation. As a by-product a measure for the lack of monotonicity of sequences is obtained. A further result refers to an inequality between the discrepancy norm and total variation which resembles Heisenberg's uncertainty relation.
- Published
- 2018