Hilbert Spaces with Reproducing Kernels and Coherent States

  • Syed Twareque Ali
  • Jean-Pierre Antoine
  • Jean-Pierre Gazeau
Part of the Graduate Texts in Contemporary Physics book series (GTCP)


This chapter is somewhat technical in nature. On the other hand, the treatment of reproducing kernel Hilbert spaces given below is rather different from that normally found in the literature, and the level of generality adopted assures immediate applicability of the concept to the various geometric and functional analytic contexts in which they are later required. Unfortunately, the level of technicality apparent in our treatment of reproducing kernels is rather high, but it was deemed necessary for the development of the theory. We have tried to lighten the reading by including illustrative examples.


Hilbert Space Vector Field Measurable Field Coherent State Positive Operator 
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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Syed Twareque Ali
    • 1
  • Jean-Pierre Antoine
    • 2
  • Jean-Pierre Gazeau
    • 3
  1. 1.Department of Mathematics and StatisticsConcordia University Loyola CampusMontréalCanada
  2. 2.Institut de Physique ThéoriqueUniversité Catholique de LouvainLouvain-la-NeuveBelgium
  3. 3.Laboratoire Physique Théoretique and Matière CondenséeUniversité de Paris 7 — Denis DiderotParisFrance

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