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Banach algebras of pseudodifferential operators and their almost diagonalization

Karlheinz Gröchenig, Ziemowit Rzeszotnik (2008)

Annales de l’institut Fourier

We define new symbol classes for pseudodifferential operators and investigate their pseudodifferential calculus. The symbol classes are parametrized by commutative convolution algebras. To every solid convolution algebra 𝒜 over a lattice Λ we associate a symbol class M , 𝒜 . Then every operator with a symbol in M , 𝒜 is almost diagonal with respect to special wave packets (coherent states or Gabor frames), and the rate of almost diagonalization is described precisely by the underlying convolution algebra...

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