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

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    ROR https://ror.org/01r9z8p25

  2. 2 Universidad Autónoma de Madrid

    Universidad Autónoma de Madrid

    Madrid, España

    ROR https://ror.org/01cby8j38

  3. 3 Universidad de Zaragoza

    Universidad de Zaragoza

    Zaragoza, España

    ROR https://ror.org/012a91z28

  4. 4 Universidad de La Rioja

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Semigroup Forum

ISSN: 0037-1912

Year of publication: 2006

Volume: 73

Issue: 1

Pages: 129-142

Type: Article

DOI: 10.1007/s00233-006-0611-8 SCOPUS: 2-s2.0-33750917589 WoS: 000241890900010 arXiv: 0511096 GOOGLE SCHOLAR lock_openOpen access editor
Author's full text: lock_openOpen access postprint


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.