Global functional calculus for operators on compact Lie groups

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 Gårding inequality for operators in $(\rho ,\delta )$-classes in the setting of compact Lie groups.

23 pages; minor corrections

References in corpus (5)

• Lp-Nuclearity, traces, and Grothendieck-Lidskii formula on compact Lie groups
• Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces
• Sharp Garding inequality on compact Lie groups
• On multipliers on compact Lie groups
• Critical exponent for the semilinear wave equation with scale invariant damping

Cited by in corpus (11)

• Schatten classes on compact manifolds: Kernel conditions
• Lp Fourier multipliers on compact Lie groups
• $L^p$-bounds for pseudo-differential operators on compact Lie groups
• Pseudo-differential operators associated to general type I locally compact groups
• Difference equations and pseudo-differential operators on ${\mathbb{Z}}^n$
• Ellipticity and Fredholmness of pseudo-differential operators on $\ell^2(\Zn)$
• Algebras of pseudo-differential operators acting on holomorphic Sobolev spaces
• Analytic functional calculus and Gårding inequality on graded Lie groups with applications to diffusion equations
• Expansion of traces and Dixmier traceability for global pseudo-differential operators on manifolds with boundary
• Intrinsic pseudodifferential calculi on any compact Lie group
• Global and Concrete Quantizations on General Type I Groups