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Gaussian Integral Operator between Fock Spaces
Abstract
We study Gaussian integral operators (Tf)(z)=1/π∫ℂ eαz2+βw̅ 2+γzw̅+ηz+δw̅ f(w)e−|w|2 dA(w) acting between Fock spaces ℱp and ℱq, where 0<p,q≤∞. We give complete characterizations of their boundedness and compactness in terms of explicit conditions on the parameters of the Gaussian kernel. The proofs are based on a unified approach combining reproducing-kernel estimates, atomic decompositions, and sampling sequences, together with a reduction to diagonal operators on sequence spaces. We also study Schatten-class membership on ℱ2 and compute the Hilbert--Schmidt norm explicitly.
Related
- Carleson Measures and Integral Operators on Fock--Sobolev Spaces
- Positive Toeplitz Operators Between Gaussian Mixed-Norm Fock Spaces
- Sharp Gaussian Mixed-Norm Theory for Fock Spaces
- Fock Projections between Gaussian Mixed-Norm Spaces: Full-Range Boundedness and Compactness
- Sampling and Interpolation in Gaussian Mixed-Norm Fock Spaces
BibTeX
@misc{sang2026gaussian,
title = {{Gaussian Integral Operator between Fock Spaces}},
author = {Yuanqi Sang and Liankuo Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28279},
eprint = {2610.28279},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28279},
}
RIS
TY - UNPB
TI - Gaussian Integral Operator between Fock Spaces
AU - Yuanqi Sang
AU - Liankuo Zhao
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28279
UR - https://arxiv.org/abs/2610.28279
AB - We study Gaussian integral operators (Tf)(z)=1/π∫_ℂ e^αz^2+βw̅^ 2+γzw̅+ηz+δw̅ f(w)e^−|w|^2 dA(w) acting between Fock spaces ℱ^p and ℱ^q, where 0<p,q≤∞. We give complete characterizations of their boundedness and compactness in terms of explicit conditions on the parameters of the Gaussian kernel. The proofs are based on a unified approach combining reproducing-kernel estimates, atomic decompositions, and sampling sequences, together with a reduction to diagonal operators on sequence spaces. We also study Schatten-class membership on ℱ^2 and compute the Hilbert--Schmidt norm explicitly.
ER -