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Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds

(2014) COMPTES RENDUS MATHEMATIQUE. 352(10). p.779-784
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Abstract
In this Note, we present criteria on both symbols and integral kernels ensuring that the corresponding operators on compact manifolds belong to Schatten classes. A specific test for nuclearity is established as well as the corresponding trace formulae. In the special case of compact Lie groups, kernel criteria in terms of (locally and globally) hypoelliptic operators are also given. A notion of invariant operator and its full symbol associated with an elliptic operator are introduced. Some applications to the study of r-nuclearity on L-P spaces are also obtained.
Keywords
GLOBAL HYPOELLIPTICITY, RIEMANNIAN-MANIFOLDS, LIE-GROUPS, EIGENFUNCTIONS, OPERATORS

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Citation

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

MLA
Delgado, Julio, and Michael Ruzhansky. “Kernel and Symbol Criteria for Schatten Classes and R-nuclearity on Compact Manifolds.” COMPTES RENDUS MATHEMATIQUE 352.10 (2014): 779–784. Print.
APA
Delgado, Julio, & Ruzhansky, M. (2014). Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds. COMPTES RENDUS MATHEMATIQUE, 352(10), 779–784.
Chicago author-date
Delgado, Julio, and Michael Ruzhansky. 2014. “Kernel and Symbol Criteria for Schatten Classes and R-nuclearity on Compact Manifolds.” Comptes Rendus Mathematique 352 (10): 779–784.
Chicago author-date (all authors)
Delgado, Julio, and Michael Ruzhansky. 2014. “Kernel and Symbol Criteria for Schatten Classes and R-nuclearity on Compact Manifolds.” Comptes Rendus Mathematique 352 (10): 779–784.
Vancouver
1.
Delgado J, Ruzhansky M. Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds. COMPTES RENDUS MATHEMATIQUE. 2014;352(10):779–84.
IEEE
[1]
J. Delgado and M. Ruzhansky, “Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds,” COMPTES RENDUS MATHEMATIQUE, vol. 352, no. 10, pp. 779–784, 2014.
@article{8585193,
  abstract     = {In this Note, we present criteria on both symbols and integral kernels ensuring that the corresponding operators on compact manifolds belong to Schatten classes. A specific test for nuclearity is established as well as the corresponding trace formulae. In the special case of compact Lie groups, kernel criteria in terms of (locally and globally) hypoelliptic operators are also given. A notion of invariant operator and its full symbol associated with an elliptic operator are introduced. Some applications to the study of r-nuclearity on L-P spaces are also obtained.},
  author       = {Delgado, Julio and Ruzhansky, Michael},
  issn         = {1631-073X},
  journal      = {COMPTES RENDUS MATHEMATIQUE},
  keywords     = {GLOBAL HYPOELLIPTICITY,RIEMANNIAN-MANIFOLDS,LIE-GROUPS,EIGENFUNCTIONS,OPERATORS},
  language     = {eng},
  number       = {10},
  pages        = {779--784},
  title        = {Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds},
  url          = {http://dx.doi.org/10.1016/j.crma.2014.08.012},
  volume       = {352},
  year         = {2014},
}

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