Gröchenig, Karlheinz;Strohmer, Thomas

Pseudodifferential operators on locally compact abelian groups and Sjöstrand's symbol class

J. Reine Angew. Math. Vol.613 (2007) p.121-146, Zbl:1145.47034, MR2377132


The paper is devoted to the study of pseudodifferential operators on arbitrary locally compact abelian (LCA) groups. The authors use a time-frequency technique with the emphasis on modulation spaces, Gabor frames, and Banach algebras of matrices. For LCA groups $G$ with dual group $\widehat{G}$, they introduce a symbol class $M^{\infty,1}(G,\widehat{G})$ which for the particular case of $G
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