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Eigenfunction expansions of ultradifferentiable functions and ultradistributions

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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).
Keywords
Gevrey spaces, ultradistributions, Komatsu classes, SPACES

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Please use this url to cite or link to this publication:

Chicago
Dasgupta, Aparajita, and Michael Ruzhansky. 2016. “Eigenfunction Expansions of Ultradifferentiable Functions and Ultradistributions.” Transactions of the American Mathematical Society 368 (12): 8481–8498.
APA
Dasgupta, A., & Ruzhansky, M. (2016). Eigenfunction expansions of ultradifferentiable functions and ultradistributions. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 368(12), 8481–8498.
Vancouver
1.
Dasgupta A, Ruzhansky M. Eigenfunction expansions of ultradifferentiable functions and ultradistributions. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 2016;368(12):8481–98.
MLA
Dasgupta, Aparajita, and Michael Ruzhansky. “Eigenfunction Expansions of Ultradifferentiable Functions and Ultradistributions.” TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 368.12 (2016): 8481–8498. Print.
@article{8585392,
  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).},
  author       = {Dasgupta, Aparajita and Ruzhansky, Michael},
  issn         = {0002-9947},
  journal      = {TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY},
  keywords     = {Gevrey spaces,ultradistributions,Komatsu classes,SPACES},
  language     = {eng},
  number       = {12},
  pages        = {8481--8498},
  title        = {Eigenfunction expansions of ultradifferentiable functions and ultradistributions},
  url          = {http://dx.doi.org/10.1090/tran/6765},
  volume       = {368},
  year         = {2016},
}

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