Complex Analysis and Operator Theory

, Volume 13, Issue 3, pp 1033–1058 | Cite as

Dunkl–Schrödinger Operators

  • Béchir AmriEmail author
  • Amel Hammi


In this paper, we consider the Schrödinger operators \(L_k=-\Delta _k+V\), where \(\Delta _k\) is the Dunkl–Laplace operator and V is a non-negative potential on \(\mathbb {R}^d\). We establish that \(L_k \) is essentially self-adjoint on \(C_0^\infty (\mathbb {R}^d)\). In particular, we develop a bounded \(H^\infty \)-calculus on \(L^p\) spaces for the Dunkl harmonic oscillator operator.


Self-adjoint operator Schrödinger operator Dunkl operators 

Mathematics Subject Classification

Primary 47B25 35J10 Secondary 43A32 



The authors would like to express their sincere thanks to the referee for his comments and suggestions.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesTaibah UniversityAl-Madinah Al-MunawarahSaudi Arabia
  2. 2.Faculté des sciences de Tunis, Laboratoire d’Analyse Mathématique et ApplicationsUniversité Tunis El ManarTunisTunisie

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