The complex crown for homogeneous harmonic spaces
Roberto Camporesi, Bernhard Kr\"otz
TL;DR
This paper develops a theory for holomorphic extension of eigenfunctions on homogeneous harmonic spaces, advancing understanding of their complex structures and spectral properties.
Contribution
It introduces a novel framework for holomorphic extension of eigenfunctions specifically tailored to homogeneous harmonic spaces.
Findings
Established conditions for holomorphic extension
Characterized spectral properties of eigenfunctions
Provided new insights into complex structures of harmonic spaces
Abstract
A theory of holomorphic extension of eigenfunctions on homogeneous harmonic spaces is developed.
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Taxonomy
TopicsHolomorphic and Operator Theory · Geometry and complex manifolds · Algebraic and Geometric Analysis