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Causality and a Theorem of paley and wiener
Citation Link: https://doi.org/10.15480/882.4176
Publikationstyp
Book Part
Date Issued
2022
Sprache
English
Institut
TORE-DOI
First published in
Number in series
287
Start Page
119
End Page
130
Citation
Operator Theory: Advances and Applications 287: 119-130 (2022)
Publisher DOI
Scopus ID
Publisher
Springer
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.
DDC Class
510: Mathematik
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