Schatten classes on compact manifolds: Kernel conditions☆

By J. Delgado, Michael Ruzhansky. 2014

82 citations recorded by the source corpus.

Abstract In this paper we give criteria on integral kernels ensuring that integral 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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ea2d1fb0901f8873f0376432519f4e9490c0878f

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

• Nonharmonic Analysis of Boundary Value Problems (2015, methodology): “ in [DR14a, DR14b] partly based on the ‘nonharmonic’ analysis on compact manifold by Seeley [See65, See69]. Such analysis becomes effective in a number of problems, for example it was recently used in [DR14c] to produce sharp kernel conditions for Schatten classes of operators on compact manifolds. T”
• Schatten classes and traces on compact groups (2013, background): “10 can be extended to a more general setting on compact manifolds, see [4], as well as [7] for a comparison, so the more interesting setting for us here is that of non-elliptic operators that we address in the next section.”
• Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds (2014, methodology): “Due to possible singularities of the kernel K (x, y) along the diagonal, we will require an averaging process on K , as described in [10] (see also [2,5]).”