# 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}
}
• Published 2008
• Mathematics
• Journal of Fourier Analysis and Applications
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
107 Citations

#### References

SHOWING 1-10 OF 52 REFERENCES