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Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces

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Abstract
In this paper we give global characterisations of Gevrey-Roumieu and Gevrey-Beurling spaces of ultradifferentiable functions on compact Lie groups in terms of the representation theory of the group and the spectrum of the Laplace-Beltrami operator. Furthermore, we characterise their duals, the spaces of corresponding ultradistributions. For the latter, the proof is based on first obtaining the characterisation of their alpha-duals in the sense of Kothe and the theory of sequence spaces. We also give the corresponding characterisations on compact homogeneous spaces.
Keywords
Gevrey spaces, Ultradistributions, Fourier transform, Compact Lie groups, Homogeneous spaces

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Chicago
Dasgupta, Aparajita, and Michael Ruzhansky. 2014. “Gevrey Functions and Ultradistributions on Compact Lie Groups and Homogeneous Spaces.” Bulletin Des Sciences Mathematiques 138 (6): 756–782.
APA
Dasgupta, A., & Ruzhansky, M. (2014). Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces. BULLETIN DES SCIENCES MATHEMATIQUES, 138(6), 756–782.
Vancouver
1.
Dasgupta A, Ruzhansky M. Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces. BULLETIN DES SCIENCES MATHEMATIQUES. 2014;138(6):756–82.
MLA
Dasgupta, Aparajita, and Michael Ruzhansky. “Gevrey Functions and Ultradistributions on Compact Lie Groups and Homogeneous Spaces.” BULLETIN DES SCIENCES MATHEMATIQUES 138.6 (2014): 756–782. Print.
@article{8585191,
  abstract     = {In this paper we give global characterisations of Gevrey-Roumieu and Gevrey-Beurling spaces of ultradifferentiable functions on compact Lie groups in terms of the representation theory of the group and the spectrum of the Laplace-Beltrami operator. Furthermore, we characterise their duals, the spaces of corresponding ultradistributions. For the latter, the proof is based on first obtaining the characterisation of their alpha-duals in the sense of Kothe and the theory of sequence spaces. We also give the corresponding characterisations on compact homogeneous spaces.},
  author       = {Dasgupta, Aparajita and Ruzhansky, Michael},
  issn         = {0007-4497},
  journal      = {BULLETIN DES SCIENCES MATHEMATIQUES},
  keywords     = {Gevrey spaces,Ultradistributions,Fourier transform,Compact Lie groups,Homogeneous spaces},
  language     = {eng},
  number       = {6},
  pages        = {756--782},
  title        = {Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces},
  url          = {http://dx.doi.org/10.1016/j.bulsci.2013.12.001},
  volume       = {138},
  year         = {2014},
}

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