Revista Matemática Iberoamericana

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Volume 22, Issue 2, 2006, pp. 703–724
DOI: 10.4171/RMI/471

Time-Frequency Analysis of Sjöstrand’s Class

Karlheinz Gröchenig[1]

(1) Institut für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090, WIEN, AUSTRIA

We investigate the properties an exotic symbol class of pseudodifferential operators, Sjöstrand's class, with methods of time-frequency analysis (phase space analysis). Compared to the classical treatment, the time-frequency approach leads to striklingly simple proofs of Sjöstrand's fundamental results and to far-reaching generalizations.

Keywords: Pseudodifferential operators, exotic symbols, Wigner distribution, Gabor frame, short-time Fourier transform, spectral invariance, almost diagonalization, modulation space, Wiener’s Lemma

Gröchenig Karlheinz: Time-Frequency Analysis of Sjöstrand’s Class. Rev. Mat. Iberoamericana 22 (2006), 703-724. doi: 10.4171/RMI/471