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Extension of Berezin–Lieb Inequalities

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Excursions in Harmonic Analysis, Volume 2

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

The Berezin–Lieb inequalities provide upper and lower bounds for a partition function based on phase-space integrals that involve the Glauber–Sudarshan and Husimi representations, respectively. Generalizations of these representations have recently been introduced by the present authors, and in this article, we extend the use of these new representations to develop numerous analogs of the Berezin–Lieb inequalities that may offer improved bounds. Several examples illustrate the use of the new inequalities. Although motivated by problems in quantum mechanics, these results may also find applications in time-frequency analysis, a valuable cross-fertilization that has been profitably used at various times in the past.

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Author information

Authors and Affiliations

  1. Department of Physics and Department of Mathematics, University of Florida, Gainesville, FL, 32611, USA

    John R. Klauder

  2. Department of Physics, The Norwegian University of Science and Technology, N-7491, Trondheim, Norway

    Bo-Sture K. Skagerstam

Authors
  1. John R. Klauder
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  2. Bo-Sture K. Skagerstam
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Corresponding author

Correspondence to John R. Klauder .

Editor information

Editors and Affiliations

  1. , Department of Mathematics, University of Maryland, Norbert Wiener Center, College Park, 20742-0001, Maryland, USA

    Travis D. Andrews

  2. Norbert Wiener Center, Department of Mathematics, University of Maryland, College Park, 20742, Maryland, USA

    Radu Balan

  3. Department of Mathematics, University of Maryland, College Park, 20742-4015, Maryland, USA

    John J. Benedetto

  4. Department of Mathematics, University of Maryland, College Park, 20742-4015, Maryland, USA

    Wojciech Czaja

  5. , Department of Mathematics, University of Maryland, College Park, 20742, Maryland, USA

    Kasso A. Okoudjou

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Klauder, J.R., Skagerstam, BS.K. (2013). Extension of Berezin–Lieb Inequalities. In: Andrews, T., Balan, R., Benedetto, J., Czaja, W., Okoudjou, K. (eds) Excursions in Harmonic Analysis, Volume 2. Applied and Numerical Harmonic Analysis. Birkhäuser, Boston. https://doi.org/10.1007/978-0-8176-8379-5_13

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