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Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticity

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Abstract
In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.
Keywords
Pseudo-differential operators, compact Lie groups, microlocal analysis, elliptic operators, global hypoellipticity, Leibniz formula

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MLA
Ruzhansky, Michael, et al. “Hörmander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, vol. 20, no. 3, 2014, pp. 476–99, doi:10.1007/s00041-014-9322-9.
APA
Ruzhansky, M., Turunen, V., & Wirth, J. (2014). Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticity. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 20(3), 476–499. https://doi.org/10.1007/s00041-014-9322-9
Chicago author-date
Ruzhansky, Michael, Ville Turunen, and Jens Wirth. 2014. “Hörmander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 20 (3): 476–99. https://doi.org/10.1007/s00041-014-9322-9.
Chicago author-date (all authors)
Ruzhansky, Michael, Ville Turunen, and Jens Wirth. 2014. “Hörmander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 20 (3): 476–499. doi:10.1007/s00041-014-9322-9.
Vancouver
1.
Ruzhansky M, Turunen V, Wirth J. Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticity. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. 2014;20(3):476–99.
IEEE
[1]
M. Ruzhansky, V. Turunen, and J. Wirth, “Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticity,” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, vol. 20, no. 3, pp. 476–499, 2014.
@article{8585183,
  abstract     = {{In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.}},
  author       = {{Ruzhansky, Michael and Turunen, Ville and Wirth, Jens}},
  issn         = {{1069-5869}},
  journal      = {{JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS}},
  keywords     = {{Pseudo-differential operators,compact Lie groups,microlocal analysis,elliptic operators,global hypoellipticity,Leibniz formula}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{476--499}},
  title        = {{Hörmander class of pseudo-differential operators on compact Lie groups and global hypoellipticity}},
  url          = {{http://dx.doi.org/10.1007/s00041-014-9322-9}},
  volume       = {{20}},
  year         = {{2014}},
}

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