Pseudodifferential calculus on noncommutative tori, I. Oscillating integrals

@article{Ha2018PseudodifferentialCO,
  title={Pseudodifferential calculus on noncommutative tori, I. Oscillating integrals},
  author={Hyunsu Ha and Gihyun Lee and Raphael Ponge},
  journal={International Journal of Mathematics},
  year={2018}
}
This paper is the first part of a two-paper series whose aim is to give a thorough account on Connes’ pseudodifferential calculus on noncommutative tori. This pseudodifferential calculus has been used in numerous recent papers, but a detailed description is still missing. In this paper, we focus on constructing an oscillating integral for noncommutative tori and laying down the main functional analysis ground for understanding Connes’ pseudodifferential calculus. In particular, this allows us… 
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