PreprintarXiv licencearXiv
The strong reproducing kernel thesis for Hankel operators and the Garsia norm
Abstract
Given a reproducing kernel Hilbert space ℋ and a bounded operator T on ℋ, we say that T obeys the strong reproducing kernel thesis (SRKT) if |T|=supk|Tk|, where k ranges over the normalized reproducing kernels in ℋ. Two problems are posed. One of these is to determine which Hankel operators on the Hardy space H2 obey the SRKT. The other concerns the geometry of the unit ball of BMO with respect to the Garsia norm.
Related
- Gaussian Processes with Sample Paths in Reproducing Kernel Banach Spaces
- Norm-optimal model order reduction in reproducing kernel Hilbert spaces
- Multiplicative linear functionals on reproducing kernel Hilbert spaces
- A Framework for Supervised and Unsupervised Learning via Reproducing Kernel Hilbert Spaces
- Examples of Noncompact Quasinilpotent Hankel Operators
BibTeX
@misc{dyakonov2026strong,
title = {{The strong reproducing kernel thesis for Hankel operators and the Garsia norm}},
author = {Konstantin M. Dyakonov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.33242},
eprint = {2609.33242},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33242},
}
RIS
TY - UNPB
TI - The strong reproducing kernel thesis for Hankel operators and the Garsia norm
AU - Konstantin M. Dyakonov
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2609.33242
UR - https://arxiv.org/abs/2609.33242
AB - Given a reproducing kernel Hilbert space ℋ and a bounded operator T on ℋ, we say that T obeys the strong reproducing kernel thesis (SRKT) if |T|=sup_k|Tk|, where k ranges over the normalized reproducing kernels in ℋ. Two problems are posed. One of these is to determine which Hankel operators on the Hardy space H^2 obey the SRKT. The other concerns the geometry of the unit ball of BMO with respect to the Garsia norm.
ER -