Abstract
This chapter illustrates the use of Gabor frame analysis to derive results on the spectral properties of integral and pseudodifferential operators. In particular, we obtain a sufficient condition on the kernel of an integral operator or the symbol of a pseudodifferential operator which implies that the operator is trace-class. This result significantly improves a sufficient condition due to Daubechies and Hörmander.
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Heil, C. (2003). Integral Operators, Pseudodifferential Operators, and Gabor Frames. In: Feichtinger, H.G., Strohmer, T. (eds) Advances in Gabor Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0133-5_7
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DOI: https://doi.org/10.1007/978-1-4612-0133-5_7
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