TY - GEN
T1 - Necessary and sufficient condition for the continuity of all causal projections with applications
AU - Boche, Holger
AU - Pohl, Volker
PY - 2006
Y1 - 2006
N2 - This paper investigates projections onto the space of causal transfer functions. It gives a complete characterization of the set of functions for which these projections are bounded. This characterization is done in terms of the modulus of continuity of the functions. It is shown that the Riesz projector has the smallest operator norm among all causal projectors, and that the Riesz projector is bounded precisely for those functions for which the modulus of continuity is upper bounded by a regular majorant. Moreover, some consequences of these results for several applications are discussed.
AB - This paper investigates projections onto the space of causal transfer functions. It gives a complete characterization of the set of functions for which these projections are bounded. This characterization is done in terms of the modulus of continuity of the functions. It is shown that the Riesz projector has the smallest operator norm among all causal projectors, and that the Riesz projector is bounded precisely for those functions for which the modulus of continuity is upper bounded by a regular majorant. Moreover, some consequences of these results for several applications are discussed.
UR - http://www.scopus.com/inward/record.url?scp=34547533704&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:34547533704
SN - 1424401712
SN - 9781424401710
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5353
EP - 5358
BT - Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 45th IEEE Conference on Decision and Control 2006, CDC
Y2 - 13 December 2006 through 15 December 2006
ER -