Interpolation and duality in algebras of multipliers on the ball

  • Kenneth R. Davidson

    University of Waterloo, Canada
  • Michael Hartz

    Universität des Saarlandes, Saarbrücken, Germany
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Abstract

We study the multiplier algebras obtained as the closure of the polynomials on certain reproducing kernel Hilbert spaces on the ball of . Our results apply, in particular, to the Drury–Arveson space, the Dirichlet space and the Hardy space on the ball. We first obtain a complete description of the dual and second dual spaces of in terms of the complementary bands of Henkin and totally singular measures for . This is applied to obtain several definitive results in interpolation. In particular, we establish a sharp peak interpolation result for compact -totally null sets as well as a Pick and peak interpolation theorem. Conversely, we show that a mere interpolation set is -totally null.

Cite this article

Kenneth R. Davidson, Michael Hartz, Interpolation and duality in algebras of multipliers on the ball. J. Eur. Math. Soc. 25 (2023), no. 6, pp. 2391–2434

DOI 10.4171/JEMS/1245