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Positivity aspects of the Fantappiè transform

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Abstract

A Hilbert space approach to the classical Fantappiè transform, based on the concept of Gel'fand triples of locally convex spaces, leads to a novel proof of Martineau-Aizenberg duality theorem. A study of Fantappiè transforms of positive measures on the unit ball inC n relates ideas of realization theory of multivariate linear systems, locally convex duality and pluripotential theory. This is applied to obtain von Neumann type estimates on the joint numerical range of tuples of Hilbert space operators.

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Authors and Affiliations

  1. Department of Mathematics, Washington University, 63130, St. Louis, MI, USA

    John E. McCarthy

  2. Department of Mathematics, University of California, 93106, Santa Barbara, CA, USA

    Mihai Putinar

Authors
  1. John E. McCarthy
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  2. Mihai Putinar
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Correspondence to John E. McCarthy.

Additional information

Partially supported by National Science Foundation Grants DMS 0070639 and DMS 0322255.

Partially supported by National Science Foundation Grant DMS 0100367.

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McCarthy, J.E., Putinar, M. Positivity aspects of the Fantappiè transform. J. Anal. Math. 97, 57–82 (2005). https://doi.org/10.1007/BF02807402

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  • DOI: https://doi.org/10.1007/BF02807402

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