Please use this identifier to cite or link to this item: https://doi.org/10.15480/882.4176
Publisher DOI: 10.1007/978-3-030-89397-2_8
Title: Causality and a Theorem of paley and wiener
Language: English
Authors: Seifert, Christian  
Trostorff, Sascha 
Waurick, Marcus 
Issue Date: 28-Sep-2021
Publisher: Springer
Source: Operator Theory: Advances and Applications 287: 119-130 (2022-01-01)
Abstract (english): 
In this chapter we turn our focus back to causal operators. In Chap. 5 we found out that material laws provide a class of causal and autonomous bounded operators. In this chapter we will present another proof of this fact, which rests on a result which characterises functions in L2(ℝ; H) with support contained in the non-negative reals; the celebrated Theorem of Paley and Wiener. With the help of this theorem, which is interesting in its own right, the proof of causality for material laws becomes very easy. At a first glance it seems that holomorphy of a material law is a rather strong assumption. In the second part of this chapter, however, we shall see that in designing autonomous and causal solution operators, there is no way of circumventing holomorphy.
URI: http://hdl.handle.net/11420/11750
DOI: 10.15480/882.4176
ISBN: 978-3-030-89397-2
978-3-030-89396-5
Institute: Mathematik E-10 
Document Type: Chapter (Book)
License: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
Part of Series: Operator theory 
Volume number: 287
Appears in Collections:Publications with fulltext

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