---
res:
  bibo_abstract:
  - "<jats:title>Abstract</jats:title><jats:p>This note is concerned with two families
    of operators related to the fractional Laplacian, the first arising from the Caffarelli-Silvestre
    extension problem and the second from the fractional heat equation. They both
    include the Poisson semigroup. We show that on a complete, connected, and non-compact
    Riemannian manifold of non-negative Ricci curvature, in both cases, the solution
    with <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^1$$</jats:tex-math><mml:math
    xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">\r\n                <mml:msup>\r\n
    \                 <mml:mi>L</mml:mi>\r\n                  <mml:mn>1</mml:mn>\r\n
    \               </mml:msup>\r\n              </mml:math></jats:alternatives></jats:inline-formula>
    initial data behaves asymptotically as the mass times the fundamental solution.
    Similar long-time convergence results remain valid on more general manifolds satisfying
    the Li-Yau two-sided estimate of the heat kernel. The situation changes drastically
    on hyperbolic space, and more generally on rank one non-compact symmetric spaces:
    we show that for the Poisson semigroup, the convergence to the Poisson kernel
    fails -but remains true under the additional assumption of radial initial data.</jats:p>@eng"
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Efthymia
      foaf_name: Papageorgiou, Efthymia
      foaf_surname: Papageorgiou
      foaf_workInfoHomepage: http://www.librecat.org/personId=100325
  bibo_doi: 10.1007/s11118-023-10109-1
  dct_date: 2023^xs_gYear
  dct_isPartOf:
  - http://id.crossref.org/issn/0926-2601
  - http://id.crossref.org/issn/1572-929X
  dct_language: eng
  dct_publisher: Springer Science and Business Media LLC@
  dct_subject:
  - Analysis
  dct_title: Large-Time Behavior of Two Families of Operators Related to the Fractional
    Laplacian on Certain Riemannian Manifolds@
...