Journal d’Analyse Mathématique

, Volume 98, Issue 1, pp 65–82

Composition and spectral invariance of pseudodifferential Operators on Modulation Spaces


DOI: 10.1007/BF02790270

Cite this article as:
Gröchenig, K. J. Anal. Math. (2006) 98: 65. doi:10.1007/BF02790270


We introduce new classes of Banach algebras of pseudodifferential operators with symbols in certain modulation spaces and investigate their composition and the functional calculus. Operators in these algebras possess the spectral invariance property on the associated family of modulation spaces. These results extend and contain Sjöstrand's theory, and they are obtained with new phase-space methods instead of “hard analysis”.

Copyright information

© The Hebrew University Magnes Press 2006

Authors and Affiliations

  1. 1.Institute of Biomathematics and BiometryGSF-National Research Center for Environment and HealthNeuherbergGermany
  2. 2.Faculty of MathematicsUniversity of ViennaWienAustria