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Commutant Lifting and Nevanlinna–Pick Interpolation in Several Variables

Integral Equations and Operator Theory volume 92, Article number: 27 (2020) Cite this article

Abstract

This paper concerns a commutant lifting theorem and a Nevanlinna–Pick type interpolation result in the setting of multipliers from vector-valued Drury–Arveson space to a large class of vector-valued reproducing kernel Hilbert spaces over the unit ball in \({\mathbb {C}}^n\). The special case of reproducing kernel Hilbert spaces includes all natural examples of Hilbert spaces like Hardy space, Bergman space and weighted Bergman spaces over the unit ball.

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Acknowledgements

The research of the second named author is supported by NBHM (National Board of Higher Mathematics, India) post-doctoral Fellowship No: 0204/27-/2019/R&D-II/12966. The research of the third named author is supported in part by NBHM Grant NBHM/R.P.64/2014, and the Mathematical Research Impact Centric Support (MATRICS) Grant, File No: MTR/2017/000522 and Core Research Grant, File No: CRG/2019/000908, by the Science and Engineering Research Board (SERB), Department of Science & Technology (DST), Government of India. The third author also would like to thanks the Institute of Mathematics of the Romanian Academy, Bucharest, Romania, for its warm hospitality during a visit in May 2019.

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Authors and Affiliations

  1. Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, Bangalore, 560059, India

    K. D. Deepak, Deepak Kumar Pradhan & Jaydeb Sarkar

  2. Simion Stoilow Institute of Mathematics of the Romanian Academy, Calea Grivitei 21, Bucharest, 010702, Romania

    Dan Timotin

Authors
  1. K. D. Deepak
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  2. Deepak Kumar Pradhan
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  3. Jaydeb Sarkar
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  4. Dan Timotin
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Correspondence to Jaydeb Sarkar.

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Deepak, K.D., Pradhan, D.K., Sarkar, J. et al. Commutant Lifting and Nevanlinna–Pick Interpolation in Several Variables. Integr. Equ. Oper. Theory 92, 27 (2020). https://doi.org/10.1007/s00020-020-02582-9

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  • DOI: https://doi.org/10.1007/s00020-020-02582-9

Keywords

  • Commutant lifting theorem
  • Nevanlinna–Pick interpolation
  • Weighted Bergman spaces
  • Dilations
  • Multipliers

Mathematics Subject Classification

  • 30E05
  • 47A13
  • 47A20
  • 34L25
  • 47B32
  • 47B35
  • 32A35
  • 32A36
  • 32A38