An exponential kernel associated with operators that have one-dimensional self-commutators

2018/08/28 by Kevin F. Clancey, Clancey, Kevin F.
Mathematics · #Algebraic and Geometric Analysis #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.CV #math.FA

paper · pdf · doi:10.48550/arxiv.1808.09487

arxiv created 2018/08/28 · arxiv updated 2018/08/30

Abstract

The exponential kernel Eg(λ,w) = exp -\frac1π∫_ℂ \fracg(u)u-w (u-λ) da(u ), where the compactly supported bounded measurable function g satisfies 0 ≤ g≤ 1, and suitably defined for all complex λ, w, plays a role in the theory of Hilbert space operators with one-dimensional self-commutators and in the theory of quadrature domains. This article studies continuity and integral representation properties of E_g with further applications of this exponential kernel to operators with one-dimensional self-commutator.

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