What is a Sobolev space for the Laguerre function systems?

B. Bongioanni; J. L. Torrea

Studia Mathematica, Tome 192 (2009), p. 147-172 / Harvested from The Polish Digital Mathematics Library

Résumé

We discuss the concept of Sobolev space associated to the Laguerre operator $L_{α} = - y d ² / d y ² - d / d y + y / 4 + α ² / 4 y$ , y ∈ (0,∞). We show that the natural definition does not agree with the concept of potential space defined via the potentials ${(L_{α})}^{- s}$ . 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.

Publié le : 2009-01-01

Zbl 1163.42008

EUDML-ID : urn:eudml:doc:284684

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B. Bongioanni; J. L. Torrea. What is a Sobolev space for the Laguerre function systems?. Studia Mathematica, Tome 192 (2009) pp. 147-172. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm192-2-4/