1Departamento de Matemática Facultad de Ingeniería Qímica Universidad Nacional del Litoral and Instituto de Matemática Aplicada del Litoral Santa Fe 3000, Argentina 2Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid 28049 Madrid, Spain
Studia Mathematica, Tome 192 (2009) no. 2, pp. 147-172
We discuss the concept of Sobolev space associated to the
Laguerre operator
$ L_\alpha = - y\,\frac{d^2}{dy^2} - \frac{d}{dy} + \frac{y}{4}
+ \frac{\alpha^2}{4y},\ y\in (0,\infty).$
We show that the natural definition does not agree
with the concept of potential space defined via the potentials
$ (L_\alpha)^{-s}.$ An appropriate Laguerre–Sobolev space is defined
in order to achieve that coincidence. An application is given to the
almost everywhere convergence of solutions of the Schrödinger equation.
Other Laguerre operators are also considered.
Keywords:
discuss concept sobolev space associated laguerre operator alpha frac frac frac frac alpha infty natural definition does agree concept potential space defined via potentials alpha s appropriate laguerre sobolev space defined order achieve coincidence application given almost everywhere convergence solutions schr dinger equation other laguerre operators considered
Affiliations des auteurs :
B. Bongioanni
1
;
J. L. Torrea
2
1
Departamento de Matemática Facultad de Ingeniería Qímica Universidad Nacional del Litoral and Instituto de Matemática Aplicada del Litoral Santa Fe 3000, Argentina
2
Departamento de Matemáticas Facultad de Ciencias Universidad Autónoma de Madrid 28049 Madrid, Spain
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author = {B. Bongioanni and J. L. Torrea},
title = {What is a {Sobolev} space for the {Laguerre} function systems?},
journal = {Studia Mathematica},
pages = {147--172},
year = {2009},
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doi = {10.4064/sm192-2-4},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm192-2-4/}
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B. Bongioanni; J. L. Torrea. What is a Sobolev space for the Laguerre function systems?. Studia Mathematica, Tome 192 (2009) no. 2, pp. 147-172. doi: 10.4064/sm192-2-4
