Abstract
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(ℝN). 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, ∞).
Supported by CONACYT project 43432.
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© 2006 Birkhäuser Verlag Basel/Switzerland
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Rabinovich, V.S., Roch, S. (2006). The Fredholm Property of Pseudodifferential Operators with Non-smooth Symbols on Modulation Spaces. In: Dritschel, M.A. (eds) The Extended Field of Operator Theory. Operator Theory: Advances and Applications, vol 171. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7980-3_13
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DOI: https://doi.org/10.1007/978-3-7643-7980-3_13
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