Heat and Poisson semigroups for Fourier-Neumann expansions

  1. Betancor, J.J. 1
  2. Ciaurri, O. 4
  3. Martinez, T. 2
  4. Perez, M. 3
  5. Torrea, J.L. 2
  6. Varona, J.L. 4
  1. 1 Universidad de La Laguna
    info

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    GRID grid.10041.34

  2. 2 Universidad Autónoma de Madrid
    info

    Universidad Autónoma de Madrid

    Madrid, España

    GRID grid.5515.4

  3. 3 Universidad de Zaragoza
    info

    Universidad de Zaragoza

    Zaragoza, España

    GRID grid.11205.37

  4. 4 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

Revue:
Semigroup Forum

ISSN: 0037-1912

Année de publication: 2006

Volumen: 73

Número: 1

Pages: 129-142

Type: Article

Exporter: RIS
DOI: 10.1007/s00233-006-0611-8 SCOPUS: 2-s2.0-33750917589 WoS: 000241890900010 arXiv: 0511096 GOOGLE SCHOLAR lock_openAccès ouvert editor
Texte intégral de l'auteur: lock_openAccès ouvert postprint

Résumé

Given α > -1, consider the second order differential operator in (0, ∞) Lα ≡ (x2d2/dx 2 + (2α + 3)xd/dx + x2 + (α + 1) 2)(f), which appears in the theory of Bessel functions. The purpose of this paper is to develop the corresponding harmonic analysis taking L α as the analogue to the classical Laplacian. Namely we study the boundedness properties of the heat and Poisson semigroups. These boundedness properties allow us to obtain some convergence results that can be used to solve the Cauchy problem for the corresponding heat and Poisson equations. © Springer 2006.