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Weighted Subcoercive Operators on Lie Groups by A.F.M ter Elst; Derek W Robinson is a Mathematics article available to read on EtoBox.

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Let U be a continuous representation of a Lie group G on a Banach space X and a 1 , ..., a d $ an algebraic basis of the Lie algebra g of G, i.e., the a 1 , ..., a d $ together with their multi-commutators span g. Let A i =dU(a i ) denote the infinitesimal generator of the continuous one-parameter group t [ U(exp(&ta i )) and set We analyze properties of m th order differential operators dU(C)= : :; |:| m c : A : with coefficients c : # C. If L denotes the left regular representation of G in L 2 (G) then dL(C) satisfies a Ga# rding inequality on L 2 (G) if, and only if, the closure of each dU(C) generates a holomorphic semigroup S on X, the action of S z is determined by a smooth, representation independent, kernel K z which, together with its derivatives A : K z , satisfies mth order Gaussian bounds and, if U is unitary, S is quasi-contractive in an open representation independent subsector of the sector of holomorphy. Alternatively, dL(C) satisfies a Ga# rding inequality on L 2 (G) if, and only if, the closure of dL(C) generates a holomorphic, quasi-contractive, semigroup satisfying bounds These results extend to operators for which the directions a 1 , ..., a d $ are given diffe

Who reads Weighted Subcoercive Operators on Lie Groups?

Author

A.F.M ter Elst; Derek W Robinson

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-1236)

Published

1998

Language

EN

Field

Mathematics (Physical Sciences)