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 -