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

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Title: Eigenfunction expansions of ultradifferentiable functions and ultradistributions. II. Tensor representations
Authors: Dasgupta, A
Ruzhansky, M
Item Type: Journal Article
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 previous paper. 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.
Issue Date: 7-May-2018
Date of Acceptance: 3-Dec-2017
URI: http://hdl.handle.net/10044/1/55311
DOI: https://dx.doi.org/10.1090/btran/24
ISSN: 0002-9947
Publisher: American Mathematical Society
Start Page: 81
End Page: 101
Journal / Book Title: Transactions of the American Mathematical Society, Series B
Volume: 5
Issue: 4
Copyright Statement: © 2018 by the authors under Creative Commons Attribution 3.0 License (CC BY 3.0)
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
The Leverhulme Trust
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/K039407/1
RPG-2017-151
EP/R003025/1
Keywords: math.FA
math.AP
math.SP
Primary 46F05, Secondary 58J40, 22E30
0101 Pure Mathematics
General Mathematics
Notes: 21 pages
Publication Status: Published
Appears in Collections:Pure Mathematics
Mathematics
Faculty of Natural Sciences



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