PreprintCC BY-NC-ND 4.0arXiv
Characterizing variation bounding in discrete-time Hankel operators
Abstract
We investigate the k-variation bounding property of the discrete-time Hankel operator, i.e., its invariance under the set of signals with a variation (number of sign changes) of at most k. Building on existing sign-consistency criteria, it is shown that this property is equivalent to the external positivity of k+1 explicitly realized linear discrete-time systems. Thus, making the property tractable via numerical and analytic certificates. We also derive dominant-pole restrictions for the case of k=1. A three-node thermal example illustrates the results and distinguishes variation bounding from variation diminishing.
Related
- Examples of Noncompact Quasinilpotent Hankel Operators
- The strong reproducing kernel thesis for Hankel operators and the Garsia norm
- Generalization of Toeplitz + Hankel operators in the polydisc
- The Skew Commutators of Toeplitz and Hankel operators in vector-valued Hardy Space
- Small Hankel operators on weighted Besov spaces
BibTeX
@misc{liu2026characterizing,
title = {{Characterizing variation bounding in discrete-time Hankel operators}},
author = {Zijian Liu and Tom Ashani and Christian Grussler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15279},
eprint = {2609.15279},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15279},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Characterizing variation bounding in discrete-time Hankel operators
AU - Zijian Liu
AU - Tom Ashani
AU - Christian Grussler
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15279
UR - https://arxiv.org/abs/2609.15279
AB - We investigate the k-variation bounding property of the discrete-time Hankel operator, i.e., its invariance under the set of signals with a variation (number of sign changes) of at most k. Building on existing sign-consistency criteria, it is shown that this property is equivalent to the external positivity of k+1 explicitly realized linear discrete-time systems. Thus, making the property tractable via numerical and analytic certificates. We also derive dominant-pole restrictions for the case of k=1. A three-node thermal example illustrates the results and distinguishes variation bounding from variation diminishing.
ER -