On the Fourier analysis of operators on the torus
By Michael Ruzhansky, Ville T. Turunen. 2006
81 citations recorded by the source corpus.
Basic properties of Fourier integral operators on the torus \( \mathbb{T}^n = (\mathbb{R}/2\pi \mathbb{Z})^n \) are studied by using the global representations by Fourier series instead of local representations. The results can be applied in studying hyperbolic partial differential equations.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/4d914a611ae29d6785747b208ebed776af620a8f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- Michael Ruzhansky
- Niyaz Tokmagambetov
- J. Toft
- Mitsuru Sugimoto
- Naohito Tomita
- Ville T. Turunen
- J. Delgado
- Fabio Di Nicola
Citations in the corpus
- Changes of variables in modulation and Wiener amalgam spaces (2008, methodology): “We note also that canonical transforms on the torus can be viewed as a special case of Fourier series operators considered in [26].”
- Nonharmonic Analysis of Boundary Value Problems (2015, background): “The toroidal pseudo-differential calculus on all higher dimensional tori Tn, n≥ 1, as outlined in [51] and then consistently developed in [54], cannot be covered by the first order differential operator O((1)) 1 .”
- Global quantization of pseudo-differential operators on compact Lie groups, SU(2), 3-sphere, and homogeneous spaces (2008, methodology): “However, on a compact Lie groups the use of the groups structure allows one to develop a theory parallel to those of Rn and Tn in the sense that the Fourier analysis is well adopted to the underlying representation theory.”