Almost Diagonalization of Pseudodifferential Operators

  • S. Ivan TrapassoEmail author
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


In this review we focus on the almost diagonalization of pseudodifferential operators and highlight the advantages that time-frequency techniques provide here. In particular, we retrace the steps of an insightful paper by Gröchenig, who succeeded in characterizing a class of symbols previously investigated by Sjöstrand by noticing that Gabor frames almost diagonalize the corresponding Weyl operators. This approach also allows to give new and more natural proofs of related results such as boundedness of operators or algebra and Wiener properties of the symbol class. Then, we discuss some recent developments on the theme, namely an extension of these results to a more general family of pseudodifferential operators and similar outcomes for a symbol class closely related to Sjöstrand’s one.


Almost diagonalization \(\tau \)-Wigner distribution \(\tau \)-pseudodifferential operators Wiener algebras Wiener amalgam spaces modulation spaces 

2010 Mathematics Subject Classification:

47G30 35S05 42B35 81S30 


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Authors and Affiliations

  1. 1.Dipartimento di Scienze Matematiche “G. L. Lagrange”Politecnico di TorinoTorinoItaly

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