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What is a Sobolev space for the Laguerre function systems?

Tom 192 / 2009

B. Bongioanni, J. L. Torrea Studia Mathematica 192 (2009), 147-172 MSC: Primary 42B35; Secondary 42C05. DOI: 10.4064/sm192-2-4

Streszczenie

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.

Autorzy

  • B. BongioanniDepartamento de Matemática
    Facultad de Ingeniería Qímica
    Universidad Nacional del Litoral
    and
    Instituto de Matemática Aplicada del Litoral
    Santa Fe 3000, Argentina
    e-mail
  • J. L. TorreaDepartamento de Matemáticas
    Facultad de Ciencias
    Universidad Autónoma de Madrid
    28049 Madrid, Spain
    e-mail

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