PreprintCC BY-SA 4.0arXiv
Boundary Rigidity of Line-Bundle Shilov--Poisson Transforms on Bounded Symmetric Domains
Abstract
Let Ω=G/K be an irreducible bounded symmetric domain other than the unit disk, and let S be its Shilov boundary. We study the two-parameter family of Shilov--Poisson transforms between homogeneous line bundles over S and Ω. For a transform F of L2 boundary data, we determine what finite Euclidean regularity up to the full boundary ∂Ω forces in the interior. Outside five explicit exceptional parameter families, sufficiently high finite regularity forces F=0. In each exceptional family, the conclusion is an interior covariant differential equation. In the scalar Poisson--Szegő case, it yields a finite-order Graham type theorem: the stated boundary regularity forces a Bergman-harmonic function to be pluriharmonic.
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BibTeX
@misc{chen2026boundary,
title = {{Boundary Rigidity of Line-Bundle Shilov--Poisson Transforms on Bounded Symmetric Domains}},
author = {Ren-Yu Chen and Su Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08039},
eprint = {2610.08039},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08039},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Boundary Rigidity of Line-Bundle Shilov--Poisson Transforms on Bounded Symmetric Domains
AU - Ren-Yu Chen
AU - Su Liu
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08039
UR - https://arxiv.org/abs/2610.08039
AB - Let Ω=G/K be an irreducible bounded symmetric domain other than the unit disk, and let S be its Shilov boundary. We study the two-parameter family of Shilov--Poisson transforms between homogeneous line bundles over S and Ω. For a transform F of L^2 boundary data, we determine what finite Euclidean regularity up to the full boundary ∂Ω forces in the interior. Outside five explicit exceptional parameter families, sufficiently high finite regularity forces F=0. In each exceptional family, the conclusion is an interior covariant differential equation. In the scalar Poisson--Szegő case, it yields a finite-order Graham type theorem: the stated boundary regularity forces a Bergman-harmonic function to be pluriharmonic.
ER -