What is a Sobolev space for the Laguerre function systems
What is a Sobolev space for the Laguerre function systems
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DOI：
10.4064/sm192-2-4
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发表时间：
2008
影响因子：
0.8
通讯作者：
B. Bongioanni;J. Torrea
中科院分区：
文献类型：
--
作者：
B. Bongioanni;J. Torrea
本文讨论了与Laguerre算子$ L\al = - y\，\frac{d^2}{dy^2} - \frac{d}{dy} + \frac{y}{4} + \frac{\al^2}{4 y}，\quad y\in（0，\infty）相关联的Sobolev空间的概念。我们表明，自然的定义并不符合潜在的空间的概念，通过潜在的定义$（L_\al）^{-s}。定义了一个适当的Laguerre-Sobolev空间，使之具有上述重合性.给出了Schr odinger方程解的几乎处处收敛性的一个应用.其他拉盖尔运营商也被认为是。出版：Studia Math.192（2009），no.2，147- 172。
We discuss the concept of Sobolev space associated to the Laguerre operator $ L_\al = - y\,\frac{d^2}{dy^2} - \frac{d}{dy} + \frac{y}{4} + \frac{\al^2}{4y},\quad y\in (0,\infty).$ We show that the natural definition does not fit with the concept of potential space, defined via the potentials $ (L_\al)^{-s}.$ An appropriate Laguerre-Sobolev spaces are defined in order to have the mentioned coincidence. An application is given to the almost everywhere convergence of solutions of the Schr\"odinger equation. Other Laguerre operators are also considered. Published: Studia Math. 192 (2009), no. 2, 147--172.