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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References

SHOWING 1-10 OF 52 REFERENCES
On the Fourier analysis of operators on the torus
  • 61
  • PDF
Pseudo-Differential Operators and Symmetries: Background Analysis and Advanced Topics
  • 247
  • PDF
Global L2-boundedness theorems for a class of Fourier integral operators
  • 58
  • PDF
Global L 2-Boundedness Theorems for a Class of Fourier Integral Operators
  • 85
  • PDF
^{}-boundedness of pseudo-differential operators of class _{0,0}
  • 17
  • PDF
Pseudo-differential operators on Besov spaces
  • 19
  • Highly Influential
Weighted Sobolev L2 estimates for a class of Fourier integral operators
  • 28
  • PDF
Singular ordinary differential operators and pseudodifferential equations
  • 26
Spline approximation methods for multidimensional periodic pseudodifferential equations
  • 28
On compactness of commutators of multiplications and convolutions, and boundedness of pseudodifferential operators
  • 142
  • Highly Influential
...
1
2
3
4
5
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