Global functional calculus for operators on compact Lie groups

By Michael Ruzhansky, Jens Wirth. 2013

50 citations recorded by the source corpus.

Abstract In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex powers of such operators. As an application, we give a constructive symbolic proof of the Garding inequality for operators in ( ρ , δ ) -classes in the setting of compact Lie groups.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f2f0a362960d4147f5f8868c88f76606d0200227

How researchers see this paper

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In Applied Mathematics

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

In Mathematical Physics

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

Citations in the corpus

• Schatten classes on compact manifolds: Kernel conditions☆ (2014, result): “rresponding complex power of the diagonal symbol of the operator. For left-invariant operators with diagonal matrix symbols (such as Lsub or Hγ) all such approaches yield the same operators (see e.g. [RW13] for more details). Consequently, arguing in the same way as in the proof of Theorem 3.6 we ob”
• Quantization on Nilpotent Lie Groups (2016, methodology): “The functional calculus of matrix valued symbols and its operator counterpart have been also developed in [RW14].”
• $L^{p}$ -BOUNDS FOR PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS (2016, unknown): “One can check, for example using the functional calculus from [RW14], that σ ∈ S 0 ρ,δ(G), with ρ = 1 − δ.”