Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces
By Aparajita Dasgupta, Michael Ruzhansky. Bulletin des Sciences Mathématiques, 2012
55 citations recorded by the source corpus.
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 α-duals in the sense of Kothe and the theory of sequence spaces. We also give the corresponding characterisations on compact homogeneous spaces.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/10de05c6251cf00202eb4f69448773ee67c7cc0b
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In Applied Mathematics
- J. Delgado
- Michael Ruzhansky
- Veronique Fischer
- S. Tikhonov
- E. Nursultanov
- Niyaz Tokmagambetov
- Ville T. Turunen
In Mathematical Physics
- J. Delgado
- Michael Ruzhansky
- Veronique Fischer
- S. Tikhonov
- E. Nursultanov
- Niyaz Tokmagambetov
- Durvudkhan Suragan
Citations in the corpus
- Quantization on Nilpotent Lie Groups (2016, methodology): “2 can be actually extended to hold for any 0 < s < ∞, and we refer to [DR14a] for proofs and further details.”
- $L^{p}$ -BOUNDS FOR PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS (2016, methodology): “In order to deduce some consequences the following lemma proved in [DR14] will be of importance to us.”
- Nikolskii inequality and Besov, Triebel-Lizorkin, Wiener and Beurling spaces on compact homogeneous manifolds (2014, methodology): “These spaces l(Ĝ) have been already effective and were used in [DR13] to give the characterisation of Gevrey spaces (of Roumeau and Beurling types) and the corresponding spaces of ultradistributions on compact Lie groups and homogeneous spaces.”