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Erschienen in:
2007 | OriginalPaper | Buchkapitel
The Fredholm Property of Pseudodifferential Operators with Non-smooth Symbols on Modulation Spaces
verfasst von : Vladimir S. Rabinovich, Steffen Roch
Erschienen in: The Extended Field of Operator Theory
Verlag: Birkhäuser Basel
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The aim of the paper is to study the Fredholm property of pseudodifferential operators in the Sjöstrand class
OPS
w
where we consider these operators as acting on the modulation spaces
M
2,
p
(ℝ
N
). These spaces are introduced by means of a time-frequency partition of unity. The symbol class
S
w
does not involve any assumptions on the smoothness of its elements.
In terms of their limit operators, we will derive necessary and sufficient conditions for operators in
OPS
w
to be Fredholm. In particular, it will be shown that the Fredholm property and, thus, the essential spectra of operators in this class are independent of the modulation space parameter
p ∈
(1, ∞).