Integral Operators, Pseudodifferential Operators and Gabor Frames

C. Heil

School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30322-0160, USA
email: heil@math.gatech.edu

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.