Verlagslink DOI: 10.1007/978-3-030-89397-2_8
Titel: Causality and a Theorem of paley and wiener
Sprache: Englisch
Autor/Autorin: Seifert, Christian  
Trostorff, Sascha 
Waurick, Marcus 
Erscheinungs­datum: 2022
Verlag: Springer
Quellenangabe: Operator Theory: Advances and Applications 287 : 119-130 (2022)
Zusammenfassung (englisch): 
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.
DOI: 10.15480/882.4176
ISBN: 978-3-030-89397-2
Institut: Mathematik E-10 
Dokumenttyp: Kapitel (Buch)
Lizenz: CC BY 4.0 (Attribution) CC BY 4.0 (Attribution)
Teil der Schriftenreihe: Operator theory 
Bandangabe: 287
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