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A quantum Laguerre semigroup

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Abstract

In this paper we construct a quantum extension of the Laguerre semigroup and study its properties. In particular we show that it has a unique pure invariant state and any initial state converges to this invariant state. For initial states satisfying a finite energy condition, convergence is exponentially fast.

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Acknowledgements

This work started when FF visited the Department of Mathematics, University of Delhi, and was completed whilst DK and FF where visiting Indian Statistical Institute Bangalore Centre on the occasion of the Conference KBS Fest on the occasion of 75th birthday of Professor Kalyan Bidhan Sinha in December 2019. FF and DK would like to express their gratitude to ISI Bangalore for kind hospitality and lively atmosphere. All the authors acknowledge discussions with K. B. Sinha on conservativity of minimal semigroups. SS would also like to acknowledge the support provided by the SERB-MATRICS scheme (MTR/2019/000554) of the Department of Science and Technology, Govt. of India.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci 32, I - 20133, Milano, Italy

    Franco Fagnola

  2. Department of Mathematics, Satyawati College Evening (University of Delhi), Delhi-52, India

    Dharmendra Kumar

  3. Department of Mathematics, University of Delhi, South Campus, New Delhi-21, India

    Sachi Srivastava

Authors
  1. Franco Fagnola
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  2. Dharmendra Kumar
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  3. Sachi Srivastava
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Corresponding author

Correspondence to Sachi Srivastava.

Additional information

Communicated by B V Rajarama Bhat.

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Fagnola, F., Kumar, D. & Srivastava, S. A quantum Laguerre semigroup. Indian J Pure Appl Math 52, 1201–1211 (2021). https://doi.org/10.1007/s13226-021-00029-4

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