Extension problem and fractional operators: semigroups and wave equations

J. E. Galé; P. J. Miana; P. R. Stinga

Extension problem and fractional operators: semigroups and wave equations

Analysis of PDEs 2013-02-20 v2 Classical Analysis and ODEs Functional Analysis

Authors: J. E. Galé , P. J. Miana , P. R. Stinga

Abstract

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.

Keywords

operator semigroups extension theorems operator theory

Cite

@article{arxiv.1207.7203,
  title  = {Extension problem and fractional operators: semigroups and wave equations},
  author = {J. E. Galé and P. J. Miana and P. R. Stinga},
  journal= {arXiv preprint arXiv:1207.7203},
  year   = {2013}
}

Comments

19 pages, revised version, appendix added. To appear in Journal of Evolution Equations

Extension problem and fractional operators: semigroups and wave equations

Abstract

Keywords

Cite

Comments

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