Quantization of Pseudo-differential Operators on the Torus

@article{Ruzhansky2008QuantizationOP,
  title={Quantization of Pseudo-differential Operators on the Torus},
  author={Michael Ruzhansky and Ville T. Turunen},
  journal={Journal of Fourier Analysis and Applications},
  year={2008},
  volume={16},
  pages={943-982}
}
AbstractPseudo-differential and Fourier series operators on the torus ${{\mathbb{T}}^{n}}=(\Bbb{R}/2\pi\Bbb{Z})^{n}$ are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence between toroidal and Euclidean symbols of pseudo-differential operators is established. Periodization of operators and hyperbolic partial differential equations is discussed. Fourier series operators… Expand
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