Eigenfunction expansions of ultradifferentiable functions and ultradistributions
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- by Aparajita Dasgupta and Michael Ruzhansky PDF
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Abstract:
In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold $X$. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on $X$. This extends the result for analytic functions on compact manifolds by Seeley in 1969, and the characterisation of Gevrey functions and Gevrey ultradistributions on compact Lie groups and homogeneous spaces by the authors (2014).References
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Additional Information
- Aparajita Dasgupta
- Affiliation: Faculté des Sciences, École polytechnique fédérale de Lausanne, CH-1015 Lausanne, Switzerland
- MR Author ID: 837479
- Email: aparajita.dasgupta@epfl.ch
- Michael Ruzhansky
- Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
- MR Author ID: 611131
- Email: m.ruzhansky@imperial.ac.uk
- Received by editor(s): October 9, 2014
- Published electronically: January 14, 2016
- Additional Notes: The second author was supported by the EPSRC Grant EP/K039407/1 and by the Leverhulme Research Grant RPG-2014-02.
- © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 368 (2016), 8481-8498
- MSC (2010): Primary 46F05; Secondary 22E30
- DOI: https://doi.org/10.1090/tran/6765
- MathSciNet review: 3551578
Dedicated: Dedicated to the memory of Todor Gramchev (1956-2015)