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

By J. Delgado, Michael Ruzhansky. 2014

54 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/552c9aeb1784ea67c8c126e144c8e6011b6dc793

How researchers see this paper

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In Applied Mathematics

1. J. Delgado
2. Niyaz Tokmagambetov
3. Michael Ruzhansky
4. Veronique Fischer
5. Ville T. Turunen

In Mathematical Physics

1. J. Delgado
2. Niyaz Tokmagambetov
3. Michael Ruzhansky
4. Veronique Fischer

Citations in the corpus

• Schatten classes and traces on compact groups (2013, background): “On the other hand, it is possible to find such criteria assuming additional regularity of the kernel, the problem that was addressed in [7], and a comparison between kernel and symbol criteria in those cases was done in [5].”
• Nonharmonic Analysis of Boundary Value Problems (2015, methodology): “In spirit, this is similar to the global pseudo-differential analysis on closed manifolds as in [15, 16] partly based on the “nonharmonic” analysis on compact manifold by at Im prial C olege L odon on O cber 8, 2015 htp://im rn.”