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arXiv:1207.7203 [math.AP]AbstractReferencesReviewsResources

Extension problem and fractional operators: semigroups and wave equations

J. E. Galé, P. J. Miana, P. R. Stinga

Published 2012-07-31, updated 2013-02-19Version 2

We extend results of Caffarelli--Silvestre and Stinga--Torrea regarding a characterization of fractional powers of differential operators via an extension problem. Our results apply to generators of integrated families of operators, in particular to infinitesimal generators of bounded $C_0$ semigroups and operators with purely imaginary symbol. We give integral representations to the extension problem in terms of solutions to the heat equation and the wave equation.

Comments: 19 pages, revised version, appendix added. To appear in Journal of Evolution Equations
Categories: math.AP, math.CA, math.FA
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