Schatten classes and traces on compact groups

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Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds (2014, background): “of Grothendieck [Gro55] for invariant operators in terms of the full matrix-symbol. The problem of ﬁnding such criteria on diﬀerent kinds of domain is classical and has been much studied (cf. [BS77], [DR13], [DR14b], [Tof08], [BT10] and references therein). Date: July 2, 2018. The ﬁrst author was su”
Fourier multipliers, symbols, and nuclearity on compact manifolds (2014, background): “4) reduces to τA(ξ) = ξ(x)∗(Aξ)(x) = Aξ(e), (6.6) where eis the unit element of the group. We can now establish a correspondence between the two frameworks, the one in this paper and the one given in [DR13]. In the setting of compact Lie groups the unitary dual being discrete, we can enumerate the r”
Schatten classes on compact manifolds: Kernel conditions☆ (2014, methodology): “the action of non-elliptic but hypoelliptic operators. Instead of Proposition 3.3 for elliptic operators as the starting point, here we will use its analogue for hypoelliptic operators established in [DR13b], for example its analogue for sub-Laplacians on compact Lie groups G. Let us write LG = X2 1”