375 research outputs found
Local Hardy and Rellich inequalities for sums of squares of vector fields
We prove local refined versions of Hardy's and Rellich's inequalities as well
as of uncertainty principles for sums of squares of vector fields on bounded
sets of smooth manifolds under certain assumptions on the vector fields. We
also give some explicit examples, in particular, for sums of squares of vector
fields on Euclidean spaces and for sub-Laplacians on stratified Lie groups.Comment: 28 pages; substantially revised version: Hardy inequalities improved,
several versions of Rellich inequalities adde
Global functional calculus for operators on compact Lie groups
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
-classes in the setting of compact Lie groups.Comment: 23 pages; minor correction
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