Abstract
We study time-harmonic electromagnetic and acoustic waveguides, modeled by an infinite cylinder with a non-smooth cross section. We introduce an infinitesimal generator for the wave evolution along the cylinder and prove estimates of the functional calculi of these first order non-self adjoint differential operators with non-smooth coefficients. Applying our new functional calculus, we obtain a one-to-one correspondence between polynomially bounded time-harmonic waves and functions in appropriate spectral subspaces.
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Acknowledgements
The authors are greatly indebted to Lashi Bandara (University of Potsdam), Julie Rowlett (The University of Gothenburg, Chalmers University of Technology), and Grigori Rozenblum (The University of Gothenburg, Chalmers University of Technology) for helpful comments and suggestions.
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Andreas Rosén was formerly named Andreas Axelsson.
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Nursultanov, M., Rosén, A. Evolution of Time-Harmonic Electromagnetic and Acoustic Waves Along Waveguides. Integr. Equ. Oper. Theory 90, 53 (2018). https://doi.org/10.1007/s00020-018-2472-4
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DOI: https://doi.org/10.1007/s00020-018-2472-4