[Critères portant sur des symboles et noyaux pour les classes de Schatten et r-nucléarité sur les variétés compactes]
Nous présentons dans cette Note des critères sur des symboles et noyaux pour s'assurer de ce que les opérateurs correspondants sur des variétés compactes appartiennent à une classe de Schatten. Les opérateurs à trace sont considérés comme un cas spécial. Nous introduisons aussi des notions d'opérateur invariant et de symbole global associés à un opérateur elliptique et les appliquons à l'etude de la nucléarité.
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 spaces are also obtained.
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@article{CRMATH_2014__352_10_779_0,
author = {Delgado, Julio and Ruzhansky, Michael},
title = {Kernel and symbol criteria for {Schatten} classes and \protect\emph{r}-nuclearity on compact manifolds},
journal = {Comptes Rendus. Math\'ematique},
pages = {779--784},
publisher = {Elsevier},
volume = {352},
number = {10},
year = {2014},
doi = {10.1016/j.crma.2014.08.012},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2014.08.012/}
}
TY - JOUR AU - Delgado, Julio AU - Ruzhansky, Michael TI - Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds JO - Comptes Rendus. Mathématique PY - 2014 SP - 779 EP - 784 VL - 352 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2014.08.012/ DO - 10.1016/j.crma.2014.08.012 LA - en ID - CRMATH_2014__352_10_779_0 ER -
%0 Journal Article %A Delgado, Julio %A Ruzhansky, Michael %T Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds %J Comptes Rendus. Mathématique %D 2014 %P 779-784 %V 352 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2014.08.012/ %R 10.1016/j.crma.2014.08.012 %G en %F CRMATH_2014__352_10_779_0
Delgado, Julio; Ruzhansky, Michael. Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds. Comptes Rendus. Mathématique, Tome 352 (2014) no. 10, pp. 779-784. doi : 10.1016/j.crma.2014.08.012. http://www.numdam.org/articles/10.1016/j.crma.2014.08.012/
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