Fourier multipliers, symbols, and nuclearity on compact manifolds
- Author
- Julio Delgado and Michael Ruzhansky (UGent)
- Organization
- Abstract
- The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite-dimensional subspaces. As a consequence, given a compact manifold M endowed with a positive measure, we introduce a notion of the operator's full symbol adapted to the Fourier analysis relative to a fixed elliptic operator E. We give a description of Fourier multipliers, or of operators invariant relative to E. We apply these concepts to study Schatten classes of operators on L (2)(M) and to obtain a formula for the trace of trace class operators. We also apply it to provide conditions for operators between L (p) -spaces to be r-nuclear in the sense of Grothendieck.
- Keywords
- VON-NEUMANN PROPERTIES, PSEUDODIFFERENTIAL-OPERATORS, RIEMANNIAN-MANIFOLDS, SCHATTEN CLASSES, WEYL CALCULUS, SPACES, GROTHENDIECK, TRACES, NORM, LP
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8585460
- MLA
- Delgado, Julio, and Michael Ruzhansky. “Fourier Multipliers, Symbols, and Nuclearity on Compact Manifolds.” JOURNAL D ANALYSE MATHEMATIQUE, vol. 135, no. 2, 2018, pp. 757–800, doi:10.1007/s11854-018-0052-9.
- APA
- Delgado, J., & Ruzhansky, M. (2018). Fourier multipliers, symbols, and nuclearity on compact manifolds. JOURNAL D ANALYSE MATHEMATIQUE, 135(2), 757–800. https://doi.org/10.1007/s11854-018-0052-9
- Chicago author-date
- Delgado, Julio, and Michael Ruzhansky. 2018. “Fourier Multipliers, Symbols, and Nuclearity on Compact Manifolds.” JOURNAL D ANALYSE MATHEMATIQUE 135 (2): 757–800. https://doi.org/10.1007/s11854-018-0052-9.
- Chicago author-date (all authors)
- Delgado, Julio, and Michael Ruzhansky. 2018. “Fourier Multipliers, Symbols, and Nuclearity on Compact Manifolds.” JOURNAL D ANALYSE MATHEMATIQUE 135 (2): 757–800. doi:10.1007/s11854-018-0052-9.
- Vancouver
- 1.Delgado J, Ruzhansky M. Fourier multipliers, symbols, and nuclearity on compact manifolds. JOURNAL D ANALYSE MATHEMATIQUE. 2018;135(2):757–800.
- IEEE
- [1]J. Delgado and M. Ruzhansky, “Fourier multipliers, symbols, and nuclearity on compact manifolds,” JOURNAL D ANALYSE MATHEMATIQUE, vol. 135, no. 2, pp. 757–800, 2018.
@article{8585460,
abstract = {{The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite-dimensional subspaces. As a consequence, given a compact manifold M endowed with a positive measure, we introduce a notion of the operator's full symbol adapted to the Fourier analysis relative to a fixed elliptic operator E. We give a description of Fourier multipliers, or of operators invariant relative to E. We apply these concepts to study Schatten classes of operators on L (2)(M) and to obtain a formula for the trace of trace class operators. We also apply it to provide conditions for operators between L (p) -spaces to be r-nuclear in the sense of Grothendieck.}},
author = {{Delgado, Julio and Ruzhansky, Michael}},
issn = {{0021-7670}},
journal = {{JOURNAL D ANALYSE MATHEMATIQUE}},
keywords = {{VON-NEUMANN PROPERTIES,PSEUDODIFFERENTIAL-OPERATORS,RIEMANNIAN-MANIFOLDS,SCHATTEN CLASSES,WEYL CALCULUS,SPACES,GROTHENDIECK,TRACES,NORM,LP}},
language = {{eng}},
number = {{2}},
pages = {{757--800}},
title = {{Fourier multipliers, symbols, and nuclearity on compact manifolds}},
url = {{http://doi.org/10.1007/s11854-018-0052-9}},
volume = {{135}},
year = {{2018}},
}
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