Pseudodifferential Operators, Gabor Frames, and Local Trigonometric Bases

R. Rochberg

Department of Mathematics, Washington University, St. Louis, Missouri
K. Tachizawa
Mathematical Institute, Tohoku University, Sendai, Japan
email: rr@math.wustl.edu

We use Gabor frames to give sufficient conditions on the symbols to ensure that the corresponding pseudodifferential operators belong to the classes. We also give estimates for the size of eigenfunctions of pseudodifferential operators. We use local trigonometric bases to approximately diagonalize elliptic pseudodifferential operators.