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Global functional calculus for operators on compact Lie groups

Research paper by Michael Ruzhansky, Jens Wirth

Indexed on: 24 Feb '14Published on: 24 Feb '14Published in: Mathematics - Functional Analysis



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 G\r{a}rding inequality for operators in $(\rho,\delta)$-classes in the setting of compact Lie groups.