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Transactions of the American Mathematical Society Series B

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Eigenfunction expansions of ultradifferentiable functions and ultradistributions. II. Tensor representations


Authors: Aparajita Dasgupta and Michael Ruzhansky
Journal: Trans. Amer. Math. Soc. Ser. B 5 (2018), 81-101
MSC (2010): Primary 46F05; Secondary 58J40, 22E30
DOI: https://doi.org/10.1090/btran/24
Published electronically: May 7, 2018
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Abstract: In this paper we analyse the structure of the spaces of coefficients of eigenfunction expansions of functions in Komatsu classes on compact manifolds, continuing the research in our paper [Trans. Amer. Math.Soc. 368 (2016), pp.8481-8498]. We prove that such spaces of Fourier coefficients are perfect sequence spaces. As a consequence we describe the tensor structure of sequential mappings on spaces of Fourier coefficients and characterise their adjoint mappings. In particular, the considered classes include spaces of analytic and Gevrey functions, as well as spaces of ultradistributions, yielding tensor representations for linear mappings between these spaces on compact manifolds.


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Additional Information

Aparajita Dasgupta
Affiliation: École polytechnique fédérale de Lausanne, Faculté des Sciences, CH-1015 Lausanne, Switzerland
Address at time of publication: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
Email: aparajita.dasgupta@epfl.ch

Michael Ruzhansky
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
Email: m.ruzhansky@imperial.ac.uk

DOI: https://doi.org/10.1090/btran/24
Keywords: Gevrey spaces, ultradistributions, Komatsu classes, compact manifolds.
Received by editor(s): July 7, 2017
Published electronically: May 7, 2018
Additional Notes: The second author was supported by the EPSRC Grants EP/K039407/1 and EP/R003025/1, and by the Leverhulme Research Grant RPG-2017-151. No new data was collected or generated during the course of this research.
Article copyright: © Copyright 2018 by the author under Creative Commons Attribution 3.0 License (CC BY 3.0)

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