Pseudodifferential Operators on Locally Compact Abelian Groups and Sjoestrand's Symbol Class

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We investigate pseudodifferential operators on arbitrary locally compact abelian groups. As symbol classes for the Kohn-Nirenberg calculus we introduce a version of Sjoestrand's class. Pseudodifferential operators with such symbols form a Banach algebra that is closed under inversion. Since "hard analysis" techniques are not available on locally compact abelian groups, a new time-frequency approach is used with the emphasis on modulation spaces, Gabor frames, and Banach algebras of matrices. Sjoestrand's original results are thus understood as a phenomenon of abstract harmonic analysis rather than "hard analysis" and are proved in their natural context and generality.

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Functional Analysis, Analysis of PDEs

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http://salesiana.dossiersoluciones.com/handle/123456789/111555

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0604294
 http://arxiv.org/abs/math/0604294

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arXiv