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The Fourier–Laplace transformation and material law operators
Citation Link: https://doi.org/10.15480/882.4174
Publikationstyp
Book Part
Date Issued
2022
Sprache
English
Institut
TORE-DOI
First published in
Number in series
287
Start Page
67
End Page
83
Citation
Operator Theory: Advances and Applications 287: 67-83 (2022)
Publisher DOI
Scopus ID
Publisher
Springer
In this chapter we introduce the Fourier–Laplace transformation and use it to define operator-valued functions of ∂t,ν; the so-called material law operators. These operators will play a crucial role when we deal with partial differential equations. In the equations of classical mathematical physics, like the heat equation, wave equation or Maxwell’s equation, the involved material parameters, such as heat conductivity or permeability of the underlying medium, are incorporated within these operators. Hence, these operators are also called “material law operators”. We start our chapter by defining the Fourier transformation and proving Plancherel’s theorem in the Hilbert space-valued case, which states that the Fourier transformation defines a unitary operator on L2(ℝ; H).
DDC Class
510: Mathematik
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