Extension problem and fractional operators: semigroups and wave equations
Extension problem and fractional operators: semigroups and wave equations
复制标题
DOI：
10.1007/s00028-013-0182-6
复制
发表时间：
2012-07
影响因子：
1.4
通讯作者：
J. Galé;Pedro J. Miana;P. R. Stinga
中科院分区：
文献类型：
--
作者：
J. Galé;Pedro J. Miana;P. R. Stinga
我们通过一个推广问题推广了Caffarelli-Silvestre和Stinga-Torrea关于微分算子分数次幂的刻画的结果。我们的结果适用于积分算子族的生成元，特别是有界C 0半群和纯虚符号算子的无穷小生成元。我们给积分表示的热方程和波动方程的解决方案的扩展问题。
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 boundedC0semigroups 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.