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Products of Berezin Transforms on Generalized Fock Spaces
Abstract
We study products Bα,m(d)Bβ,m(d) of Berezin transforms on generalized Fock spaces over ℂd. We establish a result for m≠2: if Bα,m(d)Bβ,m(d) coincides with another such product, then the weight parameters of the second product must be (α,β). As consequences, we characterize when two Berezin transforms commute and when the product of two Berezin transforms is again a Berezin transform.
Related
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BibTeX
@misc{tian2026products,
title = {{Products of Berezin Transforms on Generalized Fock Spaces}},
author = {Hao Tian},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14599},
eprint = {2610.14599},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14599},
}
RIS
TY - UNPB
TI - Products of Berezin Transforms on Generalized Fock Spaces
AU - Hao Tian
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14599
UR - https://arxiv.org/abs/2610.14599
AB - We study products B_α,m^(d)B_β,m^(d) of Berezin transforms on generalized Fock spaces over ℂ^d. We establish a result for m≠2: if B_α,m^(d)B_β,m^(d) coincides with another such product, then the weight parameters of the second product must be (α,β). As consequences, we characterize when two Berezin transforms commute and when the product of two Berezin transforms is again a Berezin transform.
ER -