Necessary and sufficient condition for the continuity of all causal projections with applications

Holger Boche; Volker Pohl

Necessary and sufficient condition for the continuity of all causal projections with applications

Holger Boche, Volker Pohl

Technische Universität Berlin

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

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.

Original language	English
Title of host publication	Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5353-5358
Number of pages	6
ISBN (Print)	1424401712, 9781424401710
State	Published - 2006
Externally published	Yes
Event	45th IEEE Conference on Decision and Control 2006, CDC - San Diego, CA, United States Duration: 13 Dec 2006 → 15 Dec 2006

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	45th IEEE Conference on Decision and Control 2006, CDC
Country/Territory	United States
City	San Diego, CA
Period	13/12/06 → 15/12/06

Cite this

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title = "Necessary and sufficient condition for the continuity of all causal projections with applications",

abstract = "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.",

author = "Holger Boche and Volker Pohl",

year = "2006",

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series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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note = "45th IEEE Conference on Decision and Control 2006, CDC ; Conference date: 13-12-2006 Through 15-12-2006",

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Boche, H & Pohl, V 2006, Necessary and sufficient condition for the continuity of all causal projections with applications. in Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC., 4177674, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 5353-5358, 45th IEEE Conference on Decision and Control 2006, CDC, San Diego, CA, United States, 13/12/06.

Necessary and sufficient condition for the continuity of all causal projections with applications. / Boche, Holger; Pohl, Volker.
Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC. Institute of Electrical and Electronics Engineers Inc., 2006. p. 5353-5358 4177674 (Proceedings of the IEEE Conference on Decision and Control).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Pohl, Volker

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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.

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T3 - Proceedings of the IEEE Conference on Decision and Control

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BT - Proceedings of the 45th IEEE Conference on Decision and Control 2006, CDC

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T2 - 45th IEEE Conference on Decision and Control 2006, CDC

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Necessary and sufficient condition for the continuity of all causal projections with applications

Abstract

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